Should I follow up with a recruiter on LinkedIn after I applied for a job? It's been a few weeks and the job does not appear filled/job posting has been extended.

About 2-3 weeks ago I applied for various roles (about 1-2 days after the role was posted). One was at a company in the same industry I work for (and is a direct competitor) - I really want to work there. I have not yet heard back. Usually in my field if there are enough applicants, the posting is closed; otherwise it is extended until filled. Per what I see on LinkedIn, the posting appears to have been extended; and the "actively recruiting" badge is on. I logged into the applicant tracking system, and the status is still "In progress" "under review", etc. However, I notice that it is often left at that stage until the role is eventually filled (at which time I may/may not get a rejection e mail).

Based on all this, I suspect that at the very least the internal corporate recruiter may have looked at my application, but they don't want to pursue my application due to having less experience than posted (they wanted 5, I have 4.5 spread through multiple employers) and a non-traditional career path. The role is at the same level as my current one though, so it would be a lateral move. Lack of experience was a problem with my current role - I only got my current role because an external headhunter really advocated for me to overcome the issue of less experience. I suspect they're waiting for a more ideal candidate to come along (which seems common in my field), and that they've now possibly "forgotten" about me since they already took a look.

I still want to be considered in case they decide to perhaps not be as picky. I also think that I have better chances of success if I at least have a conversation with the internal company recruiter/hiring manager (so I can address the lack of experience issue that I think is causing problems for me). Therefore, would it be appropriate to message the recruiter for the role on LinkedIn with a polite message saying:

Hi xxx,

I understand that you are recruiting for the xxx role. I applied for this role a few weeks ago. I wanted to let you know that I continue to be very interested in this role, and I do think that my background would be a good fit for the role. I am available at any time to discuss my background and experience.

Thank you for your consideration.

Best Regards,

xxx

Or would this backfire (making me seem too desperate)?

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