No. Yes.

If you are shoving a board into the soil to install the fabric, why not just use boards to edge?

But sometimes when you have an idea, you just want to try it. So try it. No harm done besides the money and the time. Maybe your dirt is really soft and your grass not too aggressive, and maybe you won't mind whatever tufts of landscape fabric will show. But I'm thinking it just won't work. Look at how grass overgrows a sidewalk. It isn't an underground barrier that you need for that purpose.

But the key is to ask yourself the purpose of your edging. In my case, the places where I have edging installed I am trying to provide a permanent boundary for grass or groundcover so that my beds retain the same carefully designed shape over the long term. This does not mean that the grass or groundcover cannot grow over the edging, as it is flush with the ground. I still need to cut the growth back, but the function of the edging is as much to provide a template for where I cut it back to as it is to keep it in bounds.

I would be annoyed by such an edging over time because (a) it wouldn't stop the grass from growing over it and then (b) you won't be able to find it to locate the right place to re-cut the edge.

Search this forum for "edging." You'll probably find more discussion of the subject than you thought was possible.

I believe you will be wasteing you time and money if you do this. I am always trying to do things "on the cheap' but draw the line when the idea will cost me a lot of hard work & only be temporary. The landscape fabric does rot anyway. Here in Tennessee, we have a lot of the flat rocks. They can be found stacked in fence rows where farmers of many years back stacked them to clear the fields of rock & also create barriers for their cattle. Here's what I do... Dig a trench about 3.5" deep & 12" wide around the beds where you want the edging. Level the trench out at the bottom & pour about 2.5" - 2" in the trench. You can get these rocks free here most of the time so I asked around & found all I needed. I then lay/level them in the sand/trench leaving them about 1.5" above the level of the ground. They are odd shaped & you can fit them together like a puzzle, nice & tight. They were free, permanent, & make a beautiful border around your beds. I did this all the way around my house & in other planting areas. I did have to buy the sand at a brick supply & picked it up in a pick-up truck. It's a lot of hard work but worth it! I am a 57 yr. old Grandma so anyone could do this.