Totally.
I commute via bike every day, and have for the last two years.
I've had commutes from 1st Ave to 9th Ave, from uptown to downtown, from downtown to uptown, and a swelteringly hot commute from 22nd St, to DUMBO, Brooklyn over the Manhattan Bridge.
Any rides on the island are a snap, almost every bridge has a bike lane, traffic is mostly slow, and bike lanes are plentiful.
Bike thieves are rampant, and parking can be difficult, so I'd strongly recommend using CitiBike, which I've used cheaply and without incident for about 4 years now.