Yes, it is best to tell the insurers. Typically, the insurers tend to rate the premium on where the car is kept most time-wise over the year so say if someone had 2 addresses, they may look to rate the premium on the address where the car is kept the most.
I have known insurers load premiums for students 'living away from home' so this is a material fact which needs to be considered by your insurers.
Sadly, our car insurance scheme starts at age 21 so we cannot help with a quote at this time.