That does work. It's the only reason I ever completed a raid.
It can also get incredibly annoying. The instant you log in, your flooded with requests; so you look like an asshole if you ignore or decline because you WANT to solo that day. Or you find an awesome group, only to discover you'll never get to play with them again ... You're just filling a slot for one of their regulars who couldn't join that day.
More often than not, I played with someone from LFG one time. It just seemed like a lot of bs to deal with just so I could raid or Nightfall. And why NF doesn't have matchmaking is beyond me.
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I think majority of the times I completed Oryx, it was with randoms because others would just get frustrated and leave... so even if it was just me, I'd always tell them that I have 3-4 people... and I don't mind the flood of requests. I usually just accept them all and forget that they're on my friends list.