simple answer is no, Suzuki use a powered antenna with an inbuilt amplifier. the "aerial" thats screwed into the base is just a bit of wire. If the amps not working then adding length isn't going to help.
Plenty of aftermarket powered antennas out there but they do require a bit of fiddling to get them to work as the connectors are propriety. This of course assumes there is power getting to it from the radio.
You can check its actually getting power, mine failed soon after buying the car and I didn't realise until i fitted a new head unit and had no radio reception at all, traced it to a bad connection in the loom at the radio plug itself.
Works great now and have had no issues with it since then.