Hmmm.. good question. I have a co-sleeper but don't actually use it, the family bed works out better for us.
I would assume that you wouldn't have anymore trouble with him crawling out of the sleeper. My guess is that he would try to crawl out through the bed and that would wake you up~~ never thought of it really!!!
I have this wooden co-sleeper and it's pretty deep~~ not as deep as a crib of course but check out the photo on the website~~ you can really tell the depth in the picture with the father and son reading~~ there's lots of rail on the sides.
HTH!
http://www.armsreach.com/product_sleigh.asp