Yes, you would have to put the binding on after you covered with the vinyl.
However, wouldn't that somewhat defeat the wipe down purpose ... as the binding could get dirty?
If you are going to cover them with vinyl, you could just skip the binding.
The fabric will be sealed in the vinyl, so you won't have to worry about it fraying.
That being said ... with you mentioning binding, are you thinking of making quilted placemats?
If so, I don't think they would seal into the vinyl very well.
If you are thinking of doing this, be sure to try it with something smaller first and see how it goes.
I am pretty sure the iron on vinyl was designed for just putting a single piece of fabric into it and nothing else.