On the CP Jaguar, it's really dependant. I've played 4 or 5 of those, some have the screw-in arm, some have the press-fit. I'm thinking the press-fit won't fit in the hole if you have a threaded bar setup as the threads flange out and might block the non-threaded arm from installing.
Not to go too far off topic, but one awesome thing I did with my CIJ Jag when I first got it was used a screw-in bar from a Washburn Wonderbar (as a screw in bar) with the regular Jaguar collet setup, worked great until I got lucky in the Guitar Center bargain bin a week later and got the bar that's on it now (true blue CIJ Jag/Jazz bar).
