Can I have a new central AC unit installed without replacing my gas furnace, which is about 25yrs old?

Well, yes you could, but,but,25 years is being very lucky and getting close to end of its life,but sometimes we have to do what we have to do

Yes. I would determine the efficiency of your current furnace and see if its worth upgrading with the new A/C, since your current furnace is near its end of life. You might get an end of season deal on a new furnace.