No it can be in a .cpp file but you just have to adhere to the fact that the handler function is referenced in the .S assembly code and thus expects the symbol name SysTick_Handler but when you’re writing the function in .cpp it by default gets a mangled symbol name that include the return type and parameter type. That has to be explicitly disabled by declaring the function to be extern "C". So just write
extern "C" void SysTick_Handler(void) {
HAL_IncTick();
}
See