Could I use a replay of a level run, an example being Green Hill Act 1, and record the replay and put it on the leaderboard?

Yes, when the leaderboards here update for Plus :)

After some discussion with the other mods for this game, unfortunately the replay system will not be accepted for IL submissions when the leaderboards update. Two reasons being that replays are broken for some people, so runs might not look right or weird, and that there is the potential of cheating. The only way to ensure that these issues don't occur is to record ILs just as how they have always been.