Applied to a job at a law firm and haven't heard back yet, can I ask the person who referred me to check with HR?

I saw a job listing at a law after it had been posted for a couple weeks and contacted someone in my network for a referral. They agreed, said they sent my resume to HR, and I applied promptly afterward. I also included their name on the appropriate spot on the application. It's been 2 weeks now and I haven't heard back from them and the company careers website says my application has been submitted and no further action is required on my part at this time. I feel like I'm a really good fit for this position and don't want to be passed up because I submitted my application a little late in the cycle. Would it be appropriate for my contact to ask HR for an update on the hiring process? I also am thinking I want to be known as the proactive and eager candidate.

I look forward to hearing the thoughts of those more experienced than me. Thank you.

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