I have 5625's (or is it 5925's) and 5945's or vice versa
and yes, you can use them just like any other servo right out of the box. That's exactly what I did on my 25% Extra.
The programmer is used for upgrading software or firmware or whatever and for things like ganging servos. If you have 3 servos controlling one surface, the programmer will allow you to fine tune them so they center and move EXACTLY the same. You can do this with linkages but the programmer gives you this flexibility.
I can't say I notice any difference flying digitals. I'm sure certain types and levels of pilots would be able to tell. I just like the fact that they are fast and strong. PLUS they're digital... they HAVE to be better!