Could you still use your sewing machine if your feed dogs were not functioning? Why or why not?

Yes, you could do free motion embroidery, quilting or darning on it, but not standard seaming.

Usually feed dogs don't work because they're dropped (look for a switch), or they're fouled with a thread jam (remove the needle plate (=throat plate) and clean thoroughly), or they haven't been lubricated in half of forever (take it in for a pro cleaning or try to DIY with a small drop of sewing machine oil.)