Headhunted for role - is it worth cold emailing employees through LinkedIn

Hi,

Current IBD analyst looking to move into PE.

You all know the usual drill. Sat at your desk, you receive an email from a recruiter/headhunter about a role. You reply send through your CV and schedule a call. Call happens, they said they’ll put forward your CV to the fund, and then nothing. Never to hear from the headhunter again. (A.K.A the fund didn’t pick your CV and the headhunter couldn’t be bothered to let you know or.. the headhunter never even put forward your CV in the first place).

I’ve recently been contacted for a role that sounds amazing and want to maximise my chances. I was thinking of trying another tactic.

Would it be worth reaching out to current people at the fund via LinkedIn informing them I’ve been headhunted and would love to arrange a call with them to ask some questions etc.. or would that be too much of a risk and those with egos get annoyed and ruin any chances you had. Or is it best to just patiently wait from the headhunter?