Cold messaging someone very senior on LinkedIn as a soon-to-be-grad?

Hello! I’m hoping to get some advice about reaching out to people on LinkedIn. I’m about to finish a PR certificate program and am beginning to look for internship opportunities. My program is well-known and respected in my area, and has a ton of industry connections.

Before Christmas, someone quite senior at an agency where I’d be very interested in working connected with me on LinkedIn. I was a bit taken aback by the request (I’m still getting used to the platform to be honest) so I am merely accepted it and moved on. I realize that I should have reached out to introduce myself then, but c’est la vie.

My question is: is it too late now for me to message this person? I’m wondering this because they’re quite senior and I’m wondering if it would even be appropriate for someone who hasn’t graduated yet to be contacting them. Like I said, I’m still pretty new to LinkedIn so don’t know the etiquette yet. My ultimate goal would be to get an internship at this agency but would also be grateful to get some more insight into agency life. I guess I don’t know how to approach this initial message.