While this article https://jazz.net/blog/index.php/2009/03/23/how-scalable-are-repository-workspaces/ is talking about Repository Workspaces in particular, Snapshots should be using the same backing data as well.

So the answer is "No, having lots of snapshots should not impact performance because RTC was designed with scalability in mind"

That being said though, I think you should evaluate why you want to do this. Like, what are you doing with snapshots (each with only 1 change set of incremental difference than the last) that cannot be done by examining the history of the components in a stream? (Since you seem to already be assuming that change sets are being added one at a time).

Even if only a small amount of data is used for each new Snapshot, if you do it A LOT, then the small amounts will add up.

Also, you might run into user workflow issues. If a dialog pops up asking you to pick a snapshot and you see hundreds of snapshot per day, then as a human day-to-day user, how do you decide what you really want?