Is it possible that a recruiter has just found the description on the net, like me, and now fishes in his network and then contacts the company once a candidate has bitten?
Yep.
I get calls on both ends like this. As a manager I get cold calls from recruiters of "I see you might have an open position... I have these people, want to give them a go?" and then I get calls from recruiters looking to use me to staff positions where they clearly know so little about the position that I'm wondering why they took a job in recruiting for technical people.
If so, are there any disadvantages for me as a possible candidate?
Wasting your time is the big one - working with a recruiter who is just going to cold call the hiring business is not any more useful than submitting your resume yourself. I'd say either one has a low probability of success.
OTOH - working with a recruiter who has an actual connection to the business as a trusted finder-of-good-people - will probaby bump your resume to a better heap, since you have someone who will be working actively with the business on your behalf and theirs.
Causing confusion is the other downside - it's a lower risk, since in a big company, or even a moderate one... the people screening incoming resumes, recruiter contacts, and such may be several different people - none of them the hiring manager. That said, if you were amazing and your resume comes to the hiring manager through a bunch of different channels, some managers will be freaked out and confused and may not follow up if they've got other good options.
What kind of questions should I ask the headhunter to find out whether he already has a relationship with the company or not?
How about: "What's your relationship with the company?" and then some follow ups for details:
- How many candidates have you placed with them
- How long have you been working with this company for this position
- What do the candidates you've placed here say about working in the business
- What details can you give me about the type of candidate they are looking for that aren't on this sheet? For example, are they looking for a particular type of personality? What's the vibe of the team? What's the management looking for in terms of cultural values? Based on who they've rejected, do you have any sense of what they don't like?
Somewhere in the midst of those details, it'll either come out they they are lying, or this is a cold call to the company.
If they answers are "we've never placed a candidate here.... they've never even interviewed any candidate we've sent..." - then it's time to say "no, really, what's the difference between applying with you and applying to this link?"
In all honesty, I never even have this conversation with most recruiters.
Even when my profiles say "not particularly interested unless the offer is amazing" (or whatever the drop down lets me pick...), I get 1 request a week. When I'm actively looking, every hit on a job board will result in 20 responses from 20 recruiters... so my activities are more on the level of triage:
1 - does this look like a form letter? I may not even keep reading
2 - is the job at all interesting? If no, move on.
3 - what value is the recruiter adding? Is this a recruiter I know? Is this a reputable firm? - then maybe I write back. If the recruiter even responds to me, then I start diagnosing both the nature of the job and the nature of the recruiter, with an eye to "do I want to take time on this?"