Absolutely, ask the SM what they will expect of you. Get to know their style, find out what they love doing and what they don't like doing (so maybe you can schedule all the costume fittings because they hate making phone calls - that's me!). You might even ask to see an old book of theirs to see what their paperwork style is. Ask if the SM has worked with the company before - if not, you'll both be trying to get into the "feel" of how that particular company likes things done. Ask the SM to describe the best ASM that they worked with in the past. Their answer will tell you a lot about the SM's priorities.
I would also recommend getting a bit of info from the production manager (or from the company in general). Maybe it would be more appropriate to ask your SM, but they may not always know. It's important to be aware of who does what (and who has more than one "official" job), what unions/professions are involved, how formally the company handles chorus/extras, video releases, stage safety (while everyone strives to be safe, some people have rigorous guidelines and others, well, just don't). Find out who orders supplies (like spike tape) and if you can be reimbursed for expenses. Find out what you're NOT allowed to do - like talk to the director/maestro/prima ballerina, or pick up props in an IA house, or swear at all in a children's theatre. Learn about the stage space so you can anticipate traffic jams and strategize scene changes. Your SM will champion most of these solutions, but you must be fully aware of the issues at hand.
I usually assign the ASM to nearly fully handle a particular area of tech, often giving them a choice between wardrobe or props. They will then generate all running sheets, check with department heads on production development, pass along rehearsal notes, etc. Turning over a department gives the ASM a sense of real ownership in part of the show, and also lets them spread their wings a little and really show what they can do when they do it "their" way instead of just following the SM like a duckling.
Like TechGal said, there are no dumb questions! Most SMs will appreciate that you're thinking ahead and being considerate enough to ask about everything from their headset etiquette to their preferred font/file type. You don't have to become a clone of your SM, but you deserve to have a solid idea of what people will expect of you. From there, just keep your eyes and ears open, and always be ready to hurry up and wait.