I saw banananana's Speedrun, and he had a maxed out pultergiest, so I am wondering if I could use my casual file to Speedrun this? Or if I need to grind coins on a separate Speedrun file?

Besides Any% and 100%, runs on this leaderboard can be performed on any file with any amount of completion. This means you would be able to use any file that already has all of the upgrades unlocked