No.
I do it all the time to lubricate it, and as long as you don't remove the little sensor (the zero-track sensor?), it doesn't matter; the drive will just move the head until it comes into that sensor, in effect recalibrating the drive (I guess?).
Anyway, if you look carefully at the back of the head, there is actually a regular, but small black spring which holds the heads together (the big copper thing the upper head is attached to is little more than a hinge, as far as I can tell), and there's three little tabs, each slightly higher than the first, where it hooks onto the upper head assembly (there may also be a few such tabs on the lower head, but I haven't done this in awhile (there's been no need), so my memory's a little fuzzy). The spring is normally hooked onto the lowest of the three tabs.
To adjust the tension, all you have to do is break the little seal (which is there to keep it from vibrating loose, I suppose) and move the spring to one of the higher tabs. As long as you don't overstretch it in the process, it should make the head as good as new.
If, even at the highest "setting", it still isn't providing enough tension, then RickNel's solution is still valid.
I hope this helps.
I don't really remember anyone on here noticing this spring before, so maybe I'm the first?
c