Generally speaking cities, especially on the East Coast, are trying to control population of pest insects, like mosquitoes, wasps, ticks and the like for the concern about blood and other diseases:
Just to mention a few.
So in the city you're likely to see mostly more benign bugs like bees, bumble bees, lady bugs, butterflies, etc. But even with the pest control that cities employs it's not perfect. So some mosquitoes will still be there, mostly around standing water and during the dusk and night time but it's not anywhere near the quantities that the OFF is advertising with.
Now when you move out of the city the suburbs may require open areas to be left in developments which could leave bug population there untouched so if you're anywhere near something like that what you will encounter is a crap shoot, so depending on where you stay and will be visiting you should plan accordingly but within DC city limits I wouldn't worry about the bug repellent.