Can other people see when I mention someone on twitter (@example)?

[this person]

Okay, so my twitter is public. I want to write someone so I thought I could send a DM (direct message) to them, but I just found out that they have to be following you for you to send it, so I decided to send a regular mention (@example) to them, but I was wondering if I did that, will it show up on other people's homepage? I can see when my friends write mentions to each other, but I have them as a follower/following. For instance I'm friends with A and B, and A mentions B, and B writes back to A. I can see both mentions, but I just realized that one of my friends was mentioning someone that I didn't have as a follower/following. For example I have friend C as a follower, but not friend D. C writes to D, but I don't see what they write until I actually go on their page. I don't remember seeing those mentions on my homepage, so I'm thinking you can only see them when you have that person as a follower/following, maybe? Not sure.

[this person]

What you write won't show up on their homepage. But if they do a simple mention or name search on themselves they should be able to find whatever you said. But they might not regularly do searches on themselves so they potentially may never see it.