Inquiring about Potential Opportunities / Jobs

By way of background, I am an investment banking analyst that is currently pursuing hedge fund roles. I have been working with the "brand-name" headhunters but my question pertains to roles at smaller hedge funds - particularly ones that aren't covered by the head hunters where networking is generally going to be the way into landing a role there. I'm thinking funds with less than $75mm.

In the situation where you don't have a contact at the fund / someone else that can put you in touch with the fund, is it admissible to send an e-mail explaining yourself, why you are interested in the fund, and within that e-mail inquiring about job opportunities / asking if they are looking to scale the current team or is this the last bit a complete no-no?

As a side note, the funds I'm thinking of are not readily near me where I can walk down the street / taxi over - more like they'd require a flight or a long-haul drive that'd take half the day. Thus I'm also trying to consider the trade-off in costs to trying to meet up with them to network.

Completely understand the aspect of networking with them to work your way in so not looking for dialogue in that regards - I have been networking with ones closer to me.

So base question is it out of line to inquire about if they are looking to bring on hire / scale in the introduction e-mail?

Appreciate any thoughts / advice / anecdotes on the subject.