After curing, the desk was very tacky
It probably wasn't cured. Something that is touch-dry after 6-12 hours in the recommended very thin coat could easily take more than a few days to stop being sticky in a thicker coat, possibly a week or longer.
Usual cause of this problem was too much being left on the surface during the application procedure. Also, as with all things like this, the ambient temperature plays a big part, drying being much more reliable and speedy when it's warm. It can be extremely retarded if the temperature is low.
I'm wondering if I might have screwed myself over by putting on this layer of wax.
Well FWIW a coat of paste was is one of the standard dodges for a sticky finish. It's not 100% effective but it can work well enough if the problem isn't too severe.
Unfortunately the best solution for this is usually to clean off the surface with plenty of solvent1 and lots of rags or paper towels. Then once the stickiness has been removed you can apply one or more additional coats of the finish the right way this time, by rubbing it in and wiping away more of the excess2
The desk had been curing for 4 days but I'm worried that this layer of wax will keep it from fully curing.
The curing of the finish is based on access to oxygen, after the initial drying phase when the spirits portion evaporates. A coat of wax isn't an air barrier so finish can dry and cure underneath it. Might be a little slowed but shouldn't make a huge difference.
Do bear in mind though that if the finish was left on too thick it probably won't ever harden up fully.
1 Because the finish isn't fully cured mineral spirits/white spirit will usually work.
2 It depends on the exact formulation of the product just how much you need to remove to get a good result and they do vary from make to make. Some are oilier than others (making them softer) and others contain more varnish (so they cure harder, usually faster too).