I would like to power my RPi2 from the 5V GPIO pin via 4 Ni-MH rechargeable batteries (4.8V) but I'm afraid about peak current. Can it somehow produce more than 2.5A? Should I use a fuse to limit that current?
The batteries won't force current through the system. Your bigger problem, though, will be running the Raspberry Pi 2 at all on 4.8 V. It's very close to under-voltage warning (which I saw quoted as 4.65V for the B+). You'll need some kind of DC-DC converter to get the voltage to consistently ≥5V.
As previously stated you need a DC-DC converter, this DROK® Electrical DC-DC Buck Voltage Converter 4.5-40V 12V To 5V/2A Step-down Volt Transformer Stabilizer Voltage Regulator Module Power Supply Switch Inverter Board with LED Voltmeter 5V USB Charger should work for you:
I got one on eBay to use with two 3.6v Lipo batteries. The 4.8v from your Ni-MH should be sufficient.