It would look really cute, but it's not necessary. If they look clean, no one will say "I'm not getting this house because the closets don't match the room." But since you are painting anyway, it's a good excuse to clean out the closets and paint them. Do whichever is less work.

I'd skip it and spend your energy elsewhere. I found there was a limit to what I could do to get ready. Tidy the closets but concentrate on things like the grout in your bath and cleaning everything like a maniac.

Unless your closets have natural light or are very well lit (and, probably, walk-in closets), I think they will look dingy if painted the wall colors of the bedrooms. Keep them white. Builder's white is not a nice white, however, so I'd find a bright, fresh white.

When I staged our house to sell, doing the closets was part of the process. Of course this added to the workload. But I did it anyway. In the case of the wall of large, deep closets in the master bedroom, all I did was seriously declutter them -- removed a very large percentage of the hanging clothes, got matching hangers for the ones that were to remain, and hung those clothes neatly, evenly spaced, and by type and color. I also vacuumed out the closets, including the floors.

In the case of a large walk-in closet, I did the same + organized the shelves above the clothes rods. The reason for limiting the work for this closet was that there was no light in it, so new, fresh paint probably would not have been noticeable. But also, the closet wasn't used much, so the older paint job still looked quite good. If there were dings or scuff marks, I'm sure I touched them up. Also, this closet's floors had always been in very bad shape. We had never planned to have those refinished and certainly were not going to do so to sell the house. So I found small rugs that covered the entire floor almost perfectly. Note that the rugs were removable, so potential buyers could see the condition of the floors if they wanted. (No permanent hiding of flaws and no preventing buyers from looking wherever they wanted to!)

However, in the case of smaller closets in other bedrooms, I emptied them completely, repainted walls and ceilings in a bright, fresh white (after a real and thorough prep that included ensuring the walls were clean & ready for painting) and replaced only about 1 percent of what had been in them. One closet contained only a neutral off-white canvas clothes storage bag (with a few items in it) and, on the storage shelf above it, a few attractive baskets covered in blue & white material with a few odds & ends in them. The blue & white fit with that room's color scheme.

The other bedroom closet contained a very small number of pieces hung on attractive hangers. I probably left something attractive on the shelf. Knowing me, it would have been something that (1) would typically be stored in a bedroom closet and (2) went with that room's color scheme.

The point was to let potential buyers see how much storage space was available in this house -- and how attractive and usable it was.

Oh, and we had a small closet on the first floor next to the coat closet. The former owner had done a DIY job by putting in cheap particle board shelves. At one point when living there I'd painted them a bright white. But then they looked just like...cheap particle board painted bright white. So I found attractive, inexpensive fabric that coordinated well with our living room stuff and covered each shelf with the stuff. That little, formerly ugly closet looked really good.

Notice that, to have closets coordinate with their rooms, I used baskets (and other items) rather than painted the closets themselves.

Finally, there was NOTHING on the floor of any closet with the exception of a few shoe racks -- again, with just a few, carefully chosen shoes in them.

The workload? If you include all the closets in the house -- and there were a lot of them -- it was enormous. But the house was a Victorian, the majority of which typically lack closet space. So I was showing off a real asset. Actually, I'd have done it regardless, as everybody talks of needing storage space....

Closets are an asset.

I realize this is a very long response to your question. For me, at the time, attic to basement staging worked out amazingly well. Whether it would today, in this market, is another question. Maybe such an effort would be pointless, I don't know. But I'd do it again anyway -- anything to make the house look as good as it could.

I am a real estate broker, & I'm in other people's houses, including their closets, all the time.

The most attractive, freshest-looking closets are the ones that are painted a bright cool white & lit with full-spectrum or ultra-bright fluorescents.

("Regular" fluorescents make things look cold & sickly, & incandescents are yellowish & dim.)

Unless there is something unusual about your closets now I wouldn't paint them. I've sold several houses after repainting and never painted the closets. Just left them white.

Here's the philosophy I subscribed to:
If my house didn't sell it was NOT going to be because of something I did not do.
I painted the inside of every closet white.
Ditto cabinets.

I painted every paintable surface in the entire house including the garage and garage ceiling.
I staged every closet and cabinet as well- each bedroom closet had a couple of garments on hangers and one pair of shoes.
Coat closet had one coat and a vacuum.
Linen closet had one set of bedding and a couple of towels.
Pantry had maybe three canned goods and a box of macaroni or something.
Under sinks in the bathrooms were similarly sparse.

It sounds extreme and it was.
But I was an extremely motivated seller.

It worked.

cearbhaill, every Realtor in the world would love you!

I generally only paint the inside of walk-in closets. If the room color is very light, I use that color. If not not, I use a fresh crisp white.

We just bought a house, and I can tell you, we did not look to see if the closets were painted or not in any of the house we looked at. We looked to see if the closets were big enough, but not whether they were painted. However, I will say, I am painting the insides of all the closets in our new house, because I want them to be super clean.