If choosing a GLOCK for shooting various speed competitions does a short barrel gun run quicker on plates and targets then a longer barrel gun ?
Comparing 34 vs 17 vs 45.....

Or does it even matter

The difference between a 17 and 34 will be negligible. You have a little more mass out front with a 34 which should equate to faster follow up shots but you're talking hundrendths of seconds.  I've shot both in competition and there wasn't a noticeable difference for me.  That said, most Production Glock shooters choose the 34 for the longer sight radius.  Unless it's your carry gun and you want to practice with it a G45 for competition use is dumb.  It offers nothing over a 17 or 34 except a shorter sight radius.

G34 all the way for the longer sight radius.  The slide cuts in the G34 result in the same weight slide as a G17.

I do prefer the way the G19X/G45 feels from a balance perspective, but I can't honestly say that I shoot it any better than the G34.