You can definitely paint fiberglass. Many older fiberglass boats are painted (when the gelcoat gives up the ghost), and, indeed, many higher end boats are now painted right from the builder, and not gelcoated at all.
A top notch job will include removing all the hardware and windows
, a good bit of prep and fairing, and then a sprayed two-part paint job. That won't come cheap, but will give you a fabulous job, that will last - and stay shiny - for decades, with care.
At the other end of the (reasonable) spectrum (not counting "broom" jobs), is a self-applied paint job, using something like a one-part Interlux Brightsides type paint, with only necessary prep and with taping off the windows
, etc. This will do the job, although the gloss retention and hardness will be nothing like a good two-part paint. The price is a fraction though.
In between are all the possible combinations of you prepping, others painting
, different types of paint, etc.
So it's kind of like saying "Can I have a suit" and then there is the range from Goodwill to a custom-made wool suit