If it will fit in the case it won't be a problem. 9.6 volts is 9.6 volts, A 2500 mah pack can produce more amperage than a 600mah pack but that's not an issue as the transmitter will only draw a specific amount and no more(unless there is a problem like an electrical short inside). So a 2500 mah pack will run longer between charges than the 600.
If the new one will fit in the case you can use it. If the new one is one of the more exotic chemistry cells then you will want to use the appropriate charger. The simple wall wart style charger can only be used with nickel cadmium or nickel metal hydride.
Anything with lithium as part of the chemical system needs to use a fancy charger to allow proper charging without damage to the pack.
Assuming that this is a Nimh pack and again assuming that you want to use the old wall wart charger that came with the set keep in mind that it was set up to charge up a 600mah pack overnight. So the charge rate will be too low to charge a 2500mah pack to full charge in that same amount of time. Instead you'll want to leave the charger connected for a good 48 hours at a time to ensure you get up to somewhere close to a full charge.
All that matters are the batteries are the same size and you end up with the same voltage. I just put a 2500 mAh battery in my Devo 10. It's actually smaller than the 8-cell battery holder that comes with the transmitter.
So yes, you can. Just make sure you have a charger that can actually charge a battery with that much capacity. A wall-wart that comes with any radio will take ages to fully charge that pack.
Also remember that if you use a LiFe, besides a charger that will charge LiFe batteries, make sure it will do a balanced charge. Even though it's a 2-cell battery, like a LiPo, it still should be properly balanced charged.
also - if you do use a LiFe or LiPo battery, don't do something stupid like I did and leave your TX on. Over discharging a lithium battery can ruin it.
I did that a few times in 5 years already BUT I was able to safely restore the packs . I did it early on when I installed LiPo packs and the first time I thought it was finished. I figured out a way to recharge it from the dead and it worked and has worked on other packs also. They don't come back 100% but all of the transmitter packs that came back are still useable today.