We've had to do it before. Although it works, it won't bale up the same way and you'll have lots of messy bits and pieces. You can square bale it, but it's tough to do. We just stacked ours and covered it up. It seemed to take longer to complete, but maybe that's because we weren't used to doing it that way. We had more time than money, though, so it was worth it to us. As for the waste, we rotated our livestock out that way to clean it up and make use of what was dropped. That might not work for everyone. I should say that my husband and I were younger then. It's tough physical work. Given a choice, I would use the proper equipment for the job, but when needs must . . .
I think you'll be fine as long as you go into it with realistic expectations.