I'd say go for it. A few months ago when I decided I was going to open a second roleplay, I was caught between an exploratory fantasy and a roleplay focused on time travel. My idea was less to do with running the course of a plot and adjusting thereafter, and more a group of people being enlisted to execute some objective that takes place at a time other than their own. Staying too long out of your own time would begin replacing your memories, because the mind simply couldn't handle such peculiar transfers through space and time for long. In other words, you disembark into another time and if you get stranded or forced to stay too long you lose yourself to it. Anyway, I found the idea appealing, and I think time travel has that sort of generally likable nature. 

My advice would be to approach simply and complicate as you go. You know, create some of the rules of time travel and world hopping and explore those a bit. Then out of nowhere a rule is broken, or something happens that really shouldn't, and things get complicated. Perhaps timelines cross (like the overlap you described), suddenly throwing things out of whack. Just have fun with it, but try to keep things straight in your own head. This sort of roleplay has a strong chance of confusing your participants, and a bit is fine, but too much may just drive others off. 

All in all good luck! This sounds like a fun idea that deserves to be shared.