Fresh in from London comes Brian DeFiore:
There's no hard and fast rule for how agencies are structured-- but you can be fairly certain that there's no 'meeting' at which agents are talking about things that they DON'T want to represent. Such a meeting would take hours and earn not a dime.
And you can also assume that the letter is structured as one person writing with the editorial "we," rather than a true indication that it speaks for everyone in the agency.
Many agencies do have a 'first reader' or a 'screener,' (in the form of an assistant/secretary) who decides which submissions the senior agent(s) should bother taking home to read. The form rejection letter you received may well have come from that person... who will see your query again if you resubmit to another agent in the shop. If you're talking about a large
agency like ICM or William Morris or Writers House, with very large staffs, it's probably not going to be noticed. If you're talking about a smaller place, it very well may.
Ultimately, there's no right or wrong here. It's going to be a personal call based on how much you want a particular agent versus how embarrassed you're going to be if you get another rejection letter marked 'like we told you the last time...' And you might.