OneDrive is like any other Windows software that you can run on your Windows PC. When it isn't doing anything, and when it's not malfunctioning, you won't even know it's running, much beyond the icon in the notification area and the entry in the processes list. However, like most other software, when it's doing something, it's going to consume resources.
If OneDrive is syncing with a Microsoft server somewhere, yes, it's going to impact your gaming "experience."
When OneDrive is not syncing, no, it's not going to affect your gaming.
OneDrive, when operating normally, shouldn't have much more syncing to perform than the changes made since the last sync, which can be reasonably often, keeping sync sizes low.
If you open Task Manager, you can see the resource usage of OneDrive. It's pretty easy to tell when it's up to something.