OP here; let me clarify what I was actually trying to determine.
I shoot an APS-C Canon DSLR and have a Canon EF zoom that tops out at 300mm.
I had the opportunity to buy a righteously-priced Canon EF-S zoom topping out at 250mm. I wanted to know if the focal length of this lens would effectively be 250mm x a 1.6 crop factor giving me essentially a 400mm lens.
I posted the fixed 200mm lens example in the OP because it was a cleaner, simpler question to respond to. It would yield the same info I wanted— but with less chance of off-topic zoom lens range/image quality/speed/flare, etc. issues muddying the thread.
Thanks to all the good info I got here, I learned that the 250 lens would in fact NOT get me any closer to the subject I was shooting. So I thanked the guy selling the EF-S lens, told him I wan’t interested and hung onto a few bucks I didn’t need to spend.
So hey guys, the next round is on me…