Yes, is the simple answer. Be sure the seed is well buried in your compost pile since, even mouldy, those seeds could germinate and some seeds have what ends up being noxious "weeds" in your garden.

Thank you for your response. The moldy bird feed are sunflower seeds,
so it would be interesting to see any survive a deep spot in the compost
pile.

I had a compost pile going on a patch of dry clay that I was trying to improve to turn into a flower bed. I made my wife promise me to throw anything organic she wanted disposed of onto that pile (except office paper). One day I came home from work to find she had dumped 5 lbs of moldy bird seed onto the pile...needless to say I spent the rest of the summer vigorously hoeing and hand weeding the new 'flower patch'.