No, trimming them will reduce your yield, not make them grow more flowers. When their growth is stunted they'll produce their normal flowers, but along whatever length their bine is. For example, if you let it grow 20', it'll produce hop cones along the top 15' or so. But if you cut it off to say, 10' you'll get cones along the top 5' of bine, but it wouldn't be the same yield condensed down, if that makes sense? Think about it. Hop farms don't trim their bines down at all, they let em grow 20' straight up because they get the most amount of hops that way.
What you can do instead, if you wish, is put up some strings and train the bines along those. Run them up about 8' of twine then horizontally across the rest of the way. They can be trained to run sideways, but you have to twist them pretty much every day in a few months when they're growing several inches a day.