Never saw a surge protector with a GFCI. What is this item - manufacturer name and model number - that addresses both anomalies?
GFCI is about not killing humans (or pets). It does nothing else.
When a GFCI does not see a same current coming back as is going out, then it assumes a human is being killed. So it cuts off power using an 'open the switch' technique that every appliance (using a mechanical or semiconductor switch) and wall switch use to power off. Power off (expected or unexpected) does not damage any appliance.
A surge protector and GFCI have nothing in common other than electricity. These are completely different devices for completely different and unrelated anomalies.