Absolutely! Wrapping top down is the way to go no matter how long the string. That definitely does make a difference, IME.
Years (years) ago was in an indie band with a tele player who wasn't super experienced. The guitar didn't have a string guide/retainer and his intonation was all over the place. I stealth restrung his guitar top down, took about five minutes. The guitar was 80% better after that. He thought I was a genius...haha.
I try to never cut my strings other than the E string on a 4 and the B string on a 5 (if necessary, usually is). It seems like a shock to the windings. I make a little v-bend in the string and cut behind that. Probably superstition.
I wind top down obviously. I like to see a lot of string on the peg to make a sharper angle at the nut. It also just looks more ... solid... to me.