I'd let ya have it...but I play 1st edition!
i dont see why not.
Smilidon was much more closely related to the lion than the tiger so I am wondering if you get one as an animal companion if he becomes a dire lion at 4th or 7th level?
In game terms a "sabertooth tiger" is a Dire Tiger (smilodon). This monster has no separate listing for stats as an animal companion, so you're pretty much stuck using the big cat companion listed under the Druid class. Mechanically speaking it is one of the very best animal companions though. As it levels up you could give it Improved Natural Attack (Bite) and Improved Critical (Bite) to help represent the big teeth.