It's just one possible criteria, but yes.
But as said, you must be careful that those aren't just discrete versions. If the timeline only gets a future version whenever someone timetravels, then that wouldn't work. Should be clear, as then the number of total separate versions of the timeline that exist is equal to the number of times that someone time traveled, which would be much less than uncountably infinite.
And, it should go without saying, but you would need to make sure that if a feat happens, it actually includes that time axis. Like, someone destroying all of spacetime should probably not be assumed to automatically include the second time axis.