I would really say that it just depends on what your worlds are. If they make sense, then I say you should go for it.
For instance, me and my friend had this one idea where both of our stories would merge at one point. In this case, both stories are in the same timeline (mine is in the present-day timeline to 3225, his is to some year in the 4000's). They way I decided to make it work is that in my story, I sent a probe to the planet that my friend's story takes place (in some odd coincidence), and he retrieves the probe, takes the information, and comes to our planet a few hundred years after my story ends.
I would say that in your case, that would actually be a pretty good idea. You could start off by giving insight into both character's worlds, then put them together in the plotline. Heck, you could even do it with some other author/writer, and create a ridiculous storyline, like one of my crazier ideas a few years back.
On a final note, merging two stories for a certain time is actually a real thing; I believe it's called a "crossover issue."
I hope this helps with your story. Good luck!