I have previously submitted mine on a grid downloaded from the website. Being a messy worker I do make a "fair" copy whe I complete the puzzle. I can't see why they would object to a photocopy, there is nothing about it in the rules, but can't give a definite answer.
You can print this off and its accepted as I won last year with a copy I'd printed off which is great, and interesting crossword, I usually print two copies and do one rough first. Good luck