He may still be able to be a double agent in Quirrel's organization.
In canon, Voldemort knew Snape reported to Dumbledore, how could he not when Snape was spared Azkaban on Dumbledore's word that Snape was a spy. Voldemort however thought that Snape reported to Dumbledore only for the advantages it gave him, personally and in the form of information to be used for the Death Eaters, and not from any true loyalty to the Light or opposition to the Death Eaters.
Similarly, Quirrelmort knows Snape serves Dumbledore, but thinks (perhaps even correctly) that Snape is also plotting and acting on his own, presumably because of some difference of opinion with the Headmaster. Quirrelmort obviously won't think him a loyal Death Eater like Voldemort did, but for that matter I doubt Quirrelmort trusts anyone who hasn't been put through what Bella has to be truly loyal. Spying on him was always going to be harder than spying on canon Voldemort, but he still may relay important information to Snape in the course of asking him the 'favors' that he wants in exchange for not informing on him to Albus. Particularly if Snape's actions weren't actually against the headmaster's orders, or if he decides to come clean about them while still pretending to Quirrel that he wants his plot to remain secret.
Quirrelmort obviously won't think him a loyal Death Eater like Voldemort did
Obviously. And this isn't because of their recent conversation, or because of the Battle of Forty-four Bullies, or because of any other difference between MoR and canon deeper than that MoR!Voldemort is not stupid.
Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: