I think you risk rejection because it's true, most agents and record companies have too many artists and not enough time - but I think you should go ahead and approach them anyway. It's like sales - you sometimes have to make a lot of calls until someone takes the bait. If you've been performing for a long time I'd send a cover letter and "resume" before sending an actual demo, listing your accomplishments, recordings, venues played, etc. It certainly wouldn't be bad manners - I mean what else can you do? It does help to have a personal connection to get you in the door but if you don't have that you've no choice but to knock. And yes, I think a lot of record companies just throw out unsolicited material, unfortunately. But I would think it's worth a try.