The pearlescent coating on your glass pearls is probably a form of plastic (or some interesting chemicals), and will most likely crack, burn or melt when you fire the polymer clay, even if you fire for the minimum time recommended on the manufacturer's package.
How about if you make your own round beads from polymer clay, instead of coating an existing bead? Then you won't have any worries about how long to fire a very thin layer, or the pearl underneath deforming or cracking.
It is easier to make a (new) round bead, then it is to evenly coat a round item with a thin layer of polymer clay.
In the jewelry & crafting worlds,
Magic-Glos is highly recommended as a glossy waterproof sealant for polymer clay. You can also use clear polyurethane varnishes (available at hardware stores) -- there are even versions for boats, so you know this is very waterproof.
Some birds are very sensitive, so although I have never heard or read that anyone's bird was harmed while polymer clay was baking, the precautions you suggest sound like a good idea.