No idea but very likely - however I do not think you have to worry as cats do not, in general eat prickly plants - at least they don't in the UK!

Many euphorbias have a milky sap which is an irritant, but as MG says your cat is unlikely to touch it. If you happen to slightly damage the plant when repotting though, be careful not to get that sap in your eyes.

Hmph! My crazy cat keeps trying to eat his brush!! Chances are, the kitty won't do anything to the plant, and vice versa, but I would keep an eye on them whenever they are together for a week or two, just in case. If you do need to contact the vet, the plant usually called "Hat Rack Cactus" is Euphorbia lactea, and you may want to google some images under that name, to make sure that that's the one. The vet will need to know the right botanical name, in order to look up proper treatment information.