Email Follow Up Before Deadline (Help!)

There is an intern position at a small vc firm posted on my school's career website. Typically, when firms host on campus interviews, the resumes, transcripts, etc, do not get sent until the deadline. However, since this firm would be interviewing on site, I believe the application materials are sent before the deadline. The official close date is April 26th.

I applied for the position through the career website last night. Would it be weird to follow up with an email to someone at the firm? If I were to follow up, I would have two options: email the general info address, or email the managing partner (only two addresses listed, small firm) The email address for the mp says, "contact address for current businesses." I was thinking of emailing the firm today to ask a) if the position is still open, and b) express my interest again/maybe attach my resume.

What do you guys think? I am really interested in this position, so I want to make sure my resume does not get lost in a pool of applicants. However, I also do not want to annoy the managing partner. Any thoughts?

Thanks!