It makes no difference to me. Who knows, the picture could've been stolen from somewhere and they could be catfish. This isn't a dating site so it would be pretty pointless to message someone based on the fact that they have an attractive/interesting profile picture. It's so shallow to message someone based on their profile pic... I'm more likely to message/interact with someone if they give attractive/interesting opinions or if I click with them or something. I also message if I have something important to say to them or if I have a question they can answer.
Absolutely makes a difference. If the initial image is crap, I won't waste my time looking at their profile.
Ex: wearing sunglasses, posing with a bunch of friends (which one are you anyway?), making a stupid face, a profile pic of your kids (I want to see YOU, not your kids), profile pic of your dog (see same reason for kids). Etc...
If she has a nice pic, I'll just put a follow, so I can get a chance of seeing it more often xD
But to actually message, it only happens when I see a good question or comment/discussion with them on some question/take. And if they do have a pic, I'll be more inclined not to message them, because I already know they receive hundreds of messages a day, and will just ignore me.
NOTE: I really hate it when people don't allow messages without having a follow on them. It's really stupid that sometimes I just want to make a curious question about something, but I have to follow them.. and when they finally accept, I obviously already forgot what I had to say... anyway...
I never message anyone first. If someone messages me I just reply and try to have a nice conversation with them regardless of how they look. Plus, you never know if the picture a person has in his/her avatar is actually them.