This is a tough call. On the one hand accounting for the time lost due to a technical issue in a legitimate run is a fair thing to do. On the other hand this brings forth a system open to abuse. There's a fair bit of RNG in this game, particularly with enemy spawns. What's to stop someone from alt+F4'ing if they get bad rng and claiming a crash? To this end I vote no to applying this rule to shorter time categories. As for lengthier runs, I can see it being allowed, but that isn't my field so I abstain from passing any kind opinion on them.
The categories are intended for ng+. At least I assume so, that's how we've been doing it on black swordsman. I suppose you could run it on new game and submit it there.
I know this game is pretty dead, but just in case anybody comes along (like I did). On the mission "The Brand's Guidance". If you go too fast through the 3rd part (after opening the first two gates) the boxes will be glitched and you'll have to wait a sec for them to be destructible. I'm not sure how fast is too fast, and if it's even a 100% guaranteed glitch. I've had this happen using the hawk of light feather on zodd, which can reach pretty insane speeds.