This is almost exactly what happens if you tilt an Xbox while it's reading a disc. (Minus botch, a word I don't know.)
There's something wrong with that, Microsoft.
Much as I'm loathed to paint Microsoft the victim, in this respect, it's the basic physics of gyroscopes that means that tilting rapidly spinning things means at least stresses in the item concerned and possibly contact with the housing.
Of course, the optical drives are usually made to withstand a degree of these kinds of forces (or at least buffer the spindle orientation sufficiently in line with the case as much as required, and the rest is relying on the CD not being so flexible as to wander too far out of concentricity, for the given RPMs it has) but, except perhaps in laptops, you generally aren't expected to pivot the case in normal use. (I do, probably more than average and certainly more than is helpful, when I need to check the stickers on the underside of machines I've currently booted up on a CD or similar. If I get the grinding noise I generally hold off and continue the operation in a slower manner, knowing that I've probably just scoured the rim of the disc but usually not done any more harm to it than the occasional careless in/out/put-on-the-desk cycle does w.r.t. significant and visible surface damage... Eventually it could be the undoing of the disc, but most are inoperable/lost/forgotten-to-be-ejected long before such roughhousing becomes critical.)
Disc surface damage, while spinning, might be from the lens-head making undue contact (I've got a dismantled optical drive sitting over on the other side of my living room, and it looks like there's been some care to make it smooth-edged at the points it might possibly impact, although I'm not sure if that's more than a fop to the issue[1]) or, in the midst of repair situations, accidentally pressing down on the optical drive's casing while it is spinning can make an interesting (and 'expensive sounding', if the discs were worth a damn) grinding noise. Which is probably why a lot of optical drives have a prominent "do not press here!" warning or similar on their top-side, especially laptop-drives which don't have anything like as much tolerance and are more likely to be seen outside of their normal host machines.
Sorry, too much technobable, I'm sure. I was originally going to say that if there are viable objections to adding reinforcing glue to the crack-area, due to weight distribution, you should also be careful with the hole-drilling procedure. Perhaps make sure that any holes you drill are partnered with a (fairly well) equidistant opposing 'repair' hole located on the other side of the spindle-hole, because removing weight from one side is as bad as adding it. There's always the possibility of drilling the hole and then in-filling it with your glue/resin (ensuring that it sits in flush to the original surface[2]) which should go some way to offsetting the difference in mass-density in the spot.
I'd perhaps not bother, for now, but then I'm not in your position and thus don't have any particular anxiousness about using the disc as is, but
do have some anxiousness that you not prematurely ruin your disc (or drive!) through following my/our advice.
[1] HDD magnetic in/out heads usually ride across the platters on little cushions that don't (until some damage/contamination gets onto it, of course) cause any issue with the platter's perpetually clean and absolutely smooth surface, and I've had HDDs work even after their covers are removed and all kinds of non-scratchy abuse applied directly to the platter-surface (e.g. drawing spirals on them with a dry-wipe pen, while they're spinning and tracking) but for removable media of any speed you often need to counteract the various vagaries of the environment by maintaining a workable air-gap. The optical head that I mentioned also has some small metal coils (partnered with either a magnet or some counterpart coils) and some springy-play, almost certainly for groove-tracking and focus-distance adjustments necessary during operation, but should keep the head off the surface as long as not subjected to too many external and inertial forces. Different makes may have a different setup and/or resilience, naturally.
[2] I'd: Put a blob in the centre, not peeping out either side. While still tacky, fill to the top and wipe flush to the surface, trying not to leave a 'flood' over on the surface. Wait a short time and turn over (not letting the flush part touch your worktop) and repeat the 'flushing' on the underside. Turn over again after another short time to ensure it's still flush, adjust as necessary. ...This all depends on the size of the drill-hole and the filler/application method used, and I've got to make the disclaimer that I've never done this with an optical disc, but instead in a not too dissimilar process used on something else so this might well still translate well. If you ever notice the "plug" dissappears from the disc, however, you may have to gamble about whether this is rattling around inside your drive, or fell out during standard de-/en-boxing operations, but certainly know that you didn't use the right material to plug the gap and withstand the disc's routine of use. Air-bubbles between initial filler and flush-fills are undesirable, and perhaps the cause of losing part of the plug, but
may not be fatally so.