Possibly the insurance would be invalidated.
From talks to insurance I pulled part of my naive view on the thing.
Story: when a couple of friends of mine where due to biennual of their national PPL and wanted to convert to EASA PPL in one go, they had to do the missing CVFR part. When the FE arrived and checked insurance coverage of the aircraft we intended to do that on, he found that insurance would not cover training. We called the insurance up for clarification and had a lengthy discussion.
Result: if it would be a sole biennual checkride, the normal insurance would cover the flight (pilot is PIC), due to the CFVR training added it is a training flight and FE is responsible for the flight (Pilot as PuT, FE is PIC) = no insurance coverage for the aircraft, but personal liability of FE. This FE had no personal insurance as a trainer to do these kind of things on non-training enrolled aircraft (or similar called by the insurance, can not remember the correct term). We where able to order a temporary extension of the insurance for one day on the phone and had to wait until the confirming fax was sent to the airfield.
I found this to be a plausible explanation and FE was happy to get some clear view as well.