In Massachusetts if you receive a ticket for unregistered car but it is insured does your insurance go up and do you get points assessed?

If the car was not properly registered, your insurance was invalid. Points are usually assessed for moving violations.

I've had this happen, in 1995, so my answer is based on the law then. I don't know if it's changed since.

The "neutral" step in MA is step 15. You get one step down for each incident-free year, up to six, which means the best you can get for insurance purposes is step 9. While no points are assessed for an unregistered vehicle citation, it counts as an "incident" and costs you an incident-free year if you otherwise had no moving violations. If you already had a moving violation in the year, the unregistered vehicle citation will have no effect on your insurance.