i don't see why not to do it go for it as long as have shown the save file your gonna play on and load that one its fine to do so

submit the run and see if it gets accepted or rejected

yes you can!, you'd just have to submit the time to the leaderboards, make sure you submit this under "NG+ Packless" so you don't have your time mixed up with the regular NG+ category :> once submitted, a moderator will verify your run and it'll be on the leaderboards for the whole world to see!