The guns themselves are held in there on springs, so no, they will not loosen. They use springs to make sure the strapping holding them in cannot be overtightened, causing the jug to crack.
Other things in there might loosen up tho - like screwdriver pots, the HV trimpots used in the focus block, possibly the centering and astigmatism sets of concentric neck magnets. How loud do you run that thang???
If you're worried about those things, perhaps gluing them fixed would be a good idea, going in.
Sony fixes all 6 of the trimpots on their focus block with a white glue - not transparent, but white - affixed to the top of each dial. Not all the way around, and not a kind of glue that would penetrate to the insides, but just a string of it on each control, such that they can be retweaked again in the future, when necessary.
Other trimpots, on boards, might change value if you hit them with glue, so maybe that's not a good idea.
The concentric neck magnets are usually already glued, either with flexible caulking, or transparent glue, which looks like Elmer's. Just a string of it, not too much. If the factory glue is still in place, no worries. If not, Elmer's works fine, both for the focus block trimpots and the neck magnets.
If your speaker is not shielded, BTW, it can tow the static convergence off if placed too close to the CRT necks, but won't affect the dynamic, or point, convergence. The misalingnment of centering is all that would be affected, and can be countered for with the centering magnets on the neck.