It’s a great idea, but as much as I loved playing Caught in a Reverie, the feeling I had when seeing the picture was more of an “meh.”/“That’s not really what my character looks like.”, than an added awesomeness.
I think it’s too easy to make the reader feel a little alienated from their character, as a premade picture will never be perfect. I don’t know if that’s a risk worth taking.
I prefer to give a character a default description and, maybe in an intro, where give the reader a choice to go off and rename/change their character or just jump straight in with the default.
In some cases, once you’re started you’re stuck with what you chose at the beginning but if there’s magic or high tech involved, you can usually find a way to allow changes at almost any time, whether it’s a magic mirror or a fancy gadget that masks your character.
As far as images go, I don’t think think there’s any way to overlay images in CS so if you have a lot of choices you’d need ridiculous numbers of images to cover them all.
But what if the MC’s really stupid? 
A default description could work… The only thing that would make me reluctant to do this is that I don’t want to give the MC a default race.
I like the profile picture idea. I might not be able til get exactly what I want, but I imagine I can find one that I’ll like enough, and it’s something different.
You could probably get around that issue by not actually mentioning race until/unless the reader actually selects one. Just leave it to the readers imagination…