Is it possible to change to a power radio antenna on a 1998 Mazda 626 that was not originally equipped that way?

You should be able to. If you buy a semi-automatic power antenna you will get a small under dash switch in the kit that will raise and lower the antenna when you press it. If you buy a fully automatic, it will turn go up and down when you turn on the radio; however, there is more wiring involved and sometimes radio disassembly. Check with larger auto stores for brands like HARADA.