That's not the perspective of any agent I've ever heard from.
A requested manuscript isn't anywhere near the slushpile. It may have come out of the slushpile, but once it's requested, it goes into a TBR queue. Granted, there are agents/agencies that operate on a strict in-line basis where things are read as they're reached, but at other places, several factors can impact where in the line a MS ends up.
Are you a celebrity? Top of the line.
Are you writing in a hot genre? Top of the line.
Do you have a referral from a client or colleague? Top of the line.
Do you have previous, paid or prestigious writing credits? Top of the line.
Did you win the partial read in a contest sponsored by the agent? Top of the line.
Is your writing solid, but maybe in a glutted or not-yet-hot genre? It's in the line, but not a priority.
Is the story solid, but the voice seems off? It's in the line, but not a priority.
Was the agent on the fence about requesting the partial? It's in the line, but not a priority.
Do you write in a tough-sell genre, even though your writing is excellent? It's in the line, but not a priority.
Is the "fit" with an editor not an obvious one for the agent? It's in the line, but not a priority.
And by priority, I mean "the things the agent can get to when he/she isn't doing work he/she is paid for." Clients come first. Their books come first. Their "could you take a look at this' partials come first.
If an agent is working on a sale or auction or contracts, etc, (or several at once) then their day is pretty full.
As to "special" projects - those are the ones the agent connects to right off. They're not waiting six months to read them because something in the writing, setting or voice clicked and they want to read it straight off.
S. Collins isn't the example you want to use for someone pulled out of the slush based on something special. She's an example of how an agent makes a great deal for an existing client. THG wasn't her first series.