Is it normal to message someone random on twitter?

In a weird way, the other day I found a girl that looks kinda... interesting. A post on Vine of hers came across my timeline. I assumed she was from around where I am, so I searched her name on Twitter and found her, figuring we'd have mutual friends, etc. This, however, was not the case.

Weirdly enough she is from Canada and I am from New England in the U.S., but regardless I think she is interesting. I was wondering if it was normal for me to strike up a conversation in hopes of becoming friends? I'm not looking for some weird kind of long distance relationship, I'm still in high school, just someone to talk to.

Also, as a side note, I follow tons of random people from all over the world on Twitter, it isn't just people I know in real life, and so do all my friends. It's kind of like a Twitter community that has similar interests to us, like music taste, etc. I'm not sure if this would make me come across as creepy because it looks like I just follow everyone.