No, but I had that toy (sort of). I had the tiger toy from the Big Jim toyline (kind of like original-era GI Joe, but more focus on the adventurer/spy stuff than the military gear) that was the original mold both the Masters of the Universe riding cats used.
By the time MotU came out, my friends and I were still collecting and playing with action figures, but not really starting new toylines (we'd discovered pick-up ballgames and riding our bikes everywhere, and soon to be D&D). I do recall seeing the He-man stuff in the collections of friend's younger siblings and having a little why-didn't-we-get-that style jealousy. I mean, we got safari heroes and white jumpsuit Buck Rogers and skinny-legged star wars toys that didn't look that much like the actors (yes, I know, would be worth hundreds in good condition today ) and they got brain breaking psycho steroid-fueled, sword-and-laser wielding, tiger-riding, lich-battling cosmic weirdness and a double shot of boy's-idea-of-manliness all in one package. If Battle Cat turned into Evel Knievel's stunt cycle and He-man had a (real, non-toothpick-thickness) lightsaber, the two of them would have been my 5-year-old perfect toy (provided it had some glow in the dark qualities and shot sparks somehow, since those seemed to be added to everything at the time).