I have absolutely no idea what the stats are for people securing agents and subsequent deals from query letters, nor do I care. This business is entirely atypical - what happens over the fence or down the road does not guarantee standardised results at your house in any way so there’s little value in making generalised statements.
I can only tell you what worked for me based on where I am now. In three weeks I'm going to London to pitch ideas and deliver scripts to Intermedia, Working Title, Material Entertainment (UK arm of New Line Cinema), World Productions (UK TV company) and, as yet to be confirmed, DNA Films, Sky TV and Dan Films - though my contact there is leaving so we'll have to see.
From what I can figure, my work is well-received, I get to pitch to the best of the best, my calls and emails get answered and it only seems to be getting better and better. I established all of these contacts through my agent who I secured with a query letter. So yeah, you can see what an utter waste of time that was.
Agent ≠ instant deal. Agents don’t get deals, they negotiate them. It’s up to the writer to charm the money out of producers via the script and the pitch. All having an agent really means is that you get to go into places you wouldn't have before and that you have to work twice as hard - a; to keep the product flowing and b; to maintain whatever contacts you establish.
Deals are insanely difficult to get for new writers but I’m far closer to making one since getting an agent than I was without. That won’t be true for everyone but, again, I refer you to what I said at the beginning – the business is atypical.
I promise that nobody will ever force you to query against your will and I don't think I or anybody else will be able to convince you about this one way or the other. But as far as I'm concerned, it worked and was worth it.
Get a hold of The First Time I Got Paid For It if you haven’t already. It’s the story of fifty writers and their first paying gigs – all of them as different from each other as chalk and cheese.
Bottom line: do what you think will work for you.