As someone who's used dozens (and dozens and dozens) of Random Morphing Potions, I think I can say NO to that.  I've gotten a Wyrae on the 3rd try, and I've gotten a Wyrae after probably 50 potions.  I've used them on just about every species except a Wyrae itself (you can't use an RMP on a Wyrae). 

Personally, I think you're more likely to get one if you're trying for a different species (i.e., when you DON'T want a Wyrae).  :D