No, the handwheel and needle should move without the bobbincase in place. The needle thread will likely hang up on the "center pin" where the bobbincase sits, but otherwise it doesn't care if that case is in place.
Are you able to post some photos? The hook area, the feed dogs, the feed dogs striking the needle plate anything that looks "wrong" to you. That way we all can see what's going on. I think it was oldsewnsew who posted a bunch of questions back on the first page. If we know the answers to those questions, we might have a better idea of where to guide you.
When you say the wheel doesn't move the needle, I see three different scenarios, each of which is treated differently.
1. Clutch knob is in "bobbin winding" mode.
2. Machine is bound up likely with thread behind the hook base, and likely the whole of the link that I posted should be gone through step by step.
3. Perhaps the handwheel can be turned, but the motor does not turn the wheel. If so, it's likely the belt needing to be tightened. Does the handwheel turn at all? wiggles a little back an forth but no actual motion? Turns smoothly or is a little reluctant?
All of these things have been suggested, but we don't really know what you've tried (besides adjusting the feed dogs) or what the actual symptoms are beyond "wheel doesn't move needle". This is akin to me to a "general car fault" - troubleshooting is possible, but not fast without more details.
I know it probably seems we're asking a lot of questions and for a lot of clarification, but it's how we "see" the problem without visuals or being there.
Featherweights are very simple machines, they don't have a lot go wrong with them. It will work, but it will take a little time to figure out what's wrong. Truthfully, the diagnostic time is always longer than the repair time.
I sincerely doubt the feed dogs themselves are at fault, I think it's something else, but with a clear photo, maybe we can help you rule that out for sure?