If by 'ok' you mean legal, then yes. If you mean is it physically possible, then yes, by all means! You can fly fish kneeling in a canoe, so sitting up in a pedal boat is a cakewalk. You're certainly higher off the water than when wading to your waist, so you can get a good backcast, even if it tends to drop a bit behind you. I expect they are plenty stable so you could even stand in it.
And yes, I'd limit it to one person unless your passenger is willing to wear a rugged PFD, a hard hat, sunglasses and a fiberglass neck guard.
(I'd also stay off moving water - rivers and such)
Troutchaser: Hah! Good point! Imagine how self-righteous a fellow could feel if he got a bit of a workout every time he went fishing!
I recall a couple of decades ago there was a woman on digdeguash lake who went out fishing in her paddleboat just about every morning at dawn. She said the fishing was good, and the winds were generally calm.