sweet peas are just that - peas They are legumes (kidney (etc.)beans, peas, peanuts). If your cham eats any part of the plant there will be no problem. Not sure what you own, but veiled are the only ones that eat vegetation regularly, though I understand that a few other species take an occasional nibble.
Sweet peas need a good amount of light so don't be surprised if they shoot up to the top and clamber all in one area. Have fun with them, they come in pretty colors, too
if you can get them to grow well they could be really nice. Just be sure to pinch off the flowers as they die so the plant can put its energy into creating more. They are annuals and require some heavy feeding so try to use natural fertilizer (like compost) rather than synthetic/miracle grow stuff. You don;t want your cham ingesting that
It depends on which sweet pea you are talking about... http://www.paghat.com/sweetpeas.html
"They are occasionally eaten, but since sweetpeas are mildly toxic & in sufficient quantities can cause disease of the nervous system, eating them is not advisable."