I have reported post after post of spam, but they don't seem to be removed. I haven't received any sort of message asking me to stop, so I keep reporting them. Does it do anything?

Yes, advertisements get removed. The Scratch Team may not remove them right away, however, depending on when they get to the report.

I'm not sure how many advertisements you've been reporting, but I wouldn't stress myself over reporting lots of advertisements. It's probably possible to report hundreds of advertising comments in a short time, if you intentionally seek out these comments over lots of projects — if you've been doing that, I'd say that's not ideal. But if you just report them as you come across them, it should be okay.