Can a gum and tooth infection cause swollen lymph nodes. Is this even possible?

Yes. Swelling of the gums and soft tissue around an infected tooth is common. If there is a lot of inflammation, or the infection is not treated, the lymph nodes that drain the area of infection will enlarge as part of the immune response, just as would happen with other infections like a cold or strep throat.
Yes. Any type of infection in the head, mouth, face and neck area can cause swollen lymph nodes.

Related Questions

Would it be possible that a gum an tooth infection cause swollen lymph nodes any dentist or people who had this?

It is possible. Any infection in an area can cause swollen nodes or glands. Consult your dentist or physician immediately for an exam. Read more...
It could. See your dentist and have that tooth evaluated and treated. Read more...