On the one hand you'd never be farther than 1.5 miles from work or home so walking wouldn't be the worse thing.

On the other hand, whose to say you wouldn't end up taking a long detour or running an errand? Look at this way: I doubt you'd ever regret getting patch kit/inflator for your bike, but you may regret not getting one. You could buy a frame mounted mini-pump if space in your pack is a concern. Patches take up very little room.