Yeah sure, if you want to burn out the motor or electronics that drive the gun out... You can't just increase the voltage in something like that all willy nilly and expect it to work. It's kind of like putting Nitrous in a car, you can't run it all the time, only in short bursts, if you ran the gun like that all the time at the higher voltage it'd kill it, especially at the greater than 200% extra voltage you wanted to give it. You might be able to get away with 1 extra cell, but it depends on if there are any real electronics inside or just simple transistors and switches.
I could offer more suggestions but I'd need good photographs of the inside of the gun and all it's electronics/electrical connections, if you feel confident enough to take the gun apart for some good pictures and put it back together then by all means do so. But if you post pictures PLEASE make sure they're well focused with at least somewhat decent lighting and not absolutely massive in size. Some people post 2048x1024 images that are so badly out of focus and dark you can't tell anything, and they're 3-4meg large.
I'm not sure if you can post images yet as you're a new user and there are some kind of posting limits for new users, but if you take them and can't post them I'll give you my e-mail address so you can send them to me and I'll post them. Up to you how much effort you want to put into it.