Electrically, yes. An AGP Pro slot can supply (a lot) more power than a regular AGP slot.
As for signalling, no. You can use a regular AGP card in an AGP Pro slot (i.e. an AGP version X card will work in an aGP Pro version X slot), but I don't think you can use an AGP Pro card in a regular AGP slot.
And no, using a normal card in a Pro slot won't absolve you of the need to use an external power connector: all those extra pins in the AGP Pro slot are the source of extra power, and normal cards don't connect to said holes.