The ENDLESS VIGIL sourcebook has the Racer talent tree that seems to allow you to get to Improved Full Throttle without having taken Full Throttle first. You can take Conditioned, then descend to Shortcut and take it, then descend to Freerunning and take it, and then take the left branch (you can go right to left, yeah? I've never seen it stated anywhere that you can't) directly to Improved Full Throttle.

Neither Full Throttle nor Improved Full Throttle are ranked, so it looks like you can just proceed to Improved Full Throttle without having to buy Full Throttle first. Does that work? And if so, can the character then technically only use the talent as described in Improved Full Throttle? (spending 1 strain to perform it as a maneuver always) Or does the character then count as having taken Full Throttle since a legal pathway allowed access to the Improved version of it already?

Thanks!

If you don't have Full Throttle, you can't use Improved FT - it modifies a talent you don't have.

Like the penguin said, generally speaking if you don't have the basic version of a talent, be it Full Throttle in the case of Improved Full Throttle or Parry/Reflect for Improved Parry/Reflect, then you get zero benefit from the Improved version, as your character doesn't have access to the ability that the Improved version references.

There's probably exceptions, but a good rule of thumb is that if an Improved talent refers to and/or modifies an ability that specifies the base talent (such as Improved Full Throttle modifying the Full Throttle action), then you need to have purchased the base talent separately.