Should I map sidewalks?

Honest answer: No. No you should not map sidewalks.

But it is an interesting question. There's no limit to the amount of detail you can add to openstreetmap. You could add a millions of nodes in the park with plant=blade_of_grass ...At some point you draw the line, and stop at some level of detail. Although this is kind of a personal choice, it's sensible to align your choice with that of other mappers, particularly other mappers around you (if there are any). It's also sensible to look at the wider area and think about how you (and others) might aim to achieve a consistent level of detail across that area. It's surprising how much detail you can gather when there's lots of people involved, but there are limits to this reasoning. The vast majority of other mappers are not mapping sidewalks.

We had a discussion about this kind of thing over on Tom Chance's blog recently. Sidewalks ('pavements') were an example I gave of a silly level of detail which we have (almost) all decided not to map.