Yep....called "mudding in"...the soil is more compact ( unless you have soil with a really lot of organic big pieces in it).
When you work very wet soil it can make big clods that will harden in the sun to almost rock like consistency, especially clay-ey soils.
But...I have done it many many times to no awful consequences. When you have time to plant, sometimes ya just gotta plant!
One time when I was overseeing the big annual beds at the arboretum, I had a crew all lined up to plant the 150 or so flats of annuals and we had a deluge the night before....like 2 1/2 inches....so we just mudded them in....and they grew...albeit more slowly.
Do what you gotta do.
Linda C

As Linda said, it's all about your soil. Pick up a handful and give it a squeeze. Do you have a blob of mud that oozes through your fingers? If yes, wait a few days. But if not you are gonna be fine. Just don't pack the soil hard around the plant - which is something you wouldn't want to do anyway. I prefer to plant on a rainy day if it is warm enough.

Add to that the compaction of the soil because of your planting activities and you've invited some problems, perhaps. Soil that is compacted while soaked often cannot recover on its own. (Remember, oxygen is every bit as important as water for plants. Compaction eliminates the large pore spaces that hold oxygen.)

Fortunately this bed is set up so that you never walk on soil. In the previous garden with clay soil we had so many problems with that, so we designed this one to have narrow sections and stepping stones wherever it is more than 3 feet wide.

I did plant maybe half a flat before it started raining again so hard I couldn't see past the drops on my glasses (maybe people without glasses can plant longer???). But in putting the soil around the roots I saw that it was almost impossible NOT to compress it. Normal firming of soil becomes something else. I remember where those ones went and this will be my test, I guess, for what I can get away with.