Don't confuse stability with strength. While the splice is strong, the nature of assembling it actually induces stress. A full splice doesn't fit together like a glove. It has to be forced together, spreading the prongs & pinching the grooves. Anybody who's ever actually made a full splice from scratch knows exactly what I'm talking about. If you do not have the pinch fit, then you have lots of glue gaps. I have seen plenty warp right across the splice, being straight above & below.
To answer the original question, yes full splice cues are more prone to be less stable, except if they are cored. As Joey pointed out, a cored piece of wood has no more internal stress pulling it one way or the other. So long as it was acclimated dry before it was drilled, then it'll stay stable. If it was not dry & acclimated before drilling, then you just wasted a piece of wood & lots of time. As it continues to dry, it'll reacquire stress. If said stress is enough to overcome the strength of the core wood, then it'll move.
Coring doesn't eliminate stress, and shouldn't be a method used to attain that goal. Core woods & host woods can have stress so there's no certainty that coring will keep wood straight. There are also plenty examples of non-cored cues that have been straight for decades or more. Staying straight has everything to do with ensuring the woods are straight, dry, acclimated, and stable to begin with. The biggest benefits or coring is controlling weight and utilizing woods that otherwise wouldn't be an option, such as burl. It will add some level of assurance that the cue will remain stable, but the woods must be stable to begin with.
In a nut shell, yes coring will increase stability, but only conditionally. Full splices that aren't cored do not have that assurance, but so long as the woods were stable to begin with, and not too much stress was induced from the splicing, then there will be no stability issues ever. The problem with any of it is that we're dealing with wood. I could make a cue here in TN and know for certain it's stable & straight, have it for years & it still be perfect, then send it to where I lived in NM and the sucker will warp. It's a possibility that we all have to live with.