Friends list

I put someone on my friends list and gave them my email address so they could put me on their list not realizing (yes, my bad) that they would be able to see when I was online at any time on any server. If I remove them from my friends list, will that remove their ability to see when I'm logged in, even though they have my email address?

Hopefully, someone knows what I'm talking about, lol.

There's just times when I want to log in and play and not have to talk to anyone, even if I do like them most of the time.