They would.That's if they actually notice him invading their minds. All Quirrel has to do is face the blackboard and start mining for information.
Legilimens is not at all subtle to the target, if you read the Occlumency training sequence in canon. To get any specific information, you do so by pushing an image into the persons's mind, reading what comes up in response, then adjusting what image/thought you push into it until they think of the right thing you want, which you can then read. There's a reason why most of the time interrogations just use Crucio.
Quirrel reading the mind of the class while working on the blackboard is going to get "man he smells funny", "this class is boring", etc.
Except for Hermione who's probably the only one focused on the subject.