Is it feasible to use a work bench without a vise for woodworking?
I have no vice and I've always been able to get by without one. In fact, in all the shows I've seen about woodworking, building houses, and doing home improvement work I cannot think of a single time I've ever seen anyone use a vice. I much more frequently use clamps anyways, which are much more versatile. 

Good woodworking is as much about using your brains to improvise as it is having the exact tools for every single job. In many cases you can build what you don't have, which are some interesting projects.