Yes. There are a couple routes he might have learned of it, though:

• Slytherin's monster, as a high-level creature keyed into the deepest wards, might be expected to know of it or be able to learn of it.
• If my speculation about the Map's anomaly is right, Voldemort's spirit could have learned of it by directly observing the twins.
• The Map has been passed down through the ages and sometimes even been in official possession, so it could be mentioned in some obscure book. Possibly it might be a headmaster secret, explaining how Dumbledore learned of it without requiring him to invade their minds.
• The twins could have been suspiciously - to Quirrel - adept at avoiding professors and obstacles, prompting him to spy on them as one would expect Quirrel to do.
• The Map could be revealed at a future date; Quirrel's suspiciously good priors have long been speculated as being related to time travel.

None of them seem especially likely, but in aggregate with other strategies I have failed to think of...