If it did, it would make it cold due to air locks or just no coolant going through the heater matrices.
When you take it into the garage, have a good look at the rear ends of the sills, the sill covers can hide a good few sins! 😮
That was my drivers side sill at the back, t'other side was similar. Worth checking and nipping in the bud sooner rather than later, i also had a hole in the passenger sill near the A pillar which was covered by the sill cover so wasn't seen by the tester at MoT time, i will be fixing it soon though. Then painting and treating, probably with :
https://www.ebay.co.uk/itm/334562128817
When it comes back into stock!