Well, yes, but my technique is going to suck just as badly regardless of whether or not I have fresh wax.
Note that leaving a fully prepped pair of skis at the start may result in ridicule if done for beer-league racing. When I was fairly serious about maximizing my performance in Killington's locals series, my habit was to ride the K-1 and use the run from the top of the lift down to the race start (near the bottom of Highline) as a warm-up run. If my skiing didn't feel like it was at 100% during that run, and time allowed for it, I'd head back up Snowdon and take a second run. I also had a fairly well-defined start routine in terms of stretching/warm up. I never did resort to carrying skis to the start, but one of the fastest guys often did (that was a line that I, personally, wasn't willing to cross for beer league).
Is that a bit much for a locals series? Probably, but we had a handful of guys who were regularly within a few tenths. There were a couple who usually led the grouping, but if they had an off day (or just didn't show up on a given Wednesday), one of the rest of us could sneak up to the top. If you care about hundredths because they make a difference in placement, it's probably worth worrying about wax. If you're more concerned with whole seconds, having waxed something reasonably close is going to matter a lot more than exactly how many runs (or how many brush strokes) go into your prep routine.