Well I'll tell you this; in my first 23 years of life, I've never had an afternoon nap, let alone fell asleep as soon as 22h. But a little over 1.5 years ago, since I started regulary working out, all that changed. It didn't change instantly, but after about 2,3 months I felt sleep was more...deserving. I not only slept longer, I slept better. Not to mention, I really enjoy a 45m nap after I get back from work and eat a proper lunch.
But I've never had insomnia or actual trouble sleeping regulary(it happened now and then). But IMO, working out regularly can only have a positive effect. You don't need to do it before sleep, just pick a time and try to be consistent in it(I workout from 16h-17h, right after work). Give it a month or two, if you ask me, it could help.