Fi and Te are two sides of the same coin. Both are related to the gut instinct too. So yeah, there is definitely a connection.
It's tough to understand what comes first...the ennneagram motivation or the cognitive functions. At least in the form of a model or a pattern than fits most people. If one is really serious about self-discovery and self-understanding one can easily see the correlations in him/herself I think. At least that has been my experience.
There is also something to be said about enneagram 9 and Fi and 8 and Te. Seeing how 9 and 8 are close to each other and are seemingly paradoxical, yet intimately related, it makes sense the whole thing is connected in some form.
8 is also the stereotype of the adult impulse and 9 of the divine child impulse.
EDIT : "Divine" child in the sense of not being tainted by worldly affairs. Still submerged in the oceanic view Freud talks about. Which explains the 9 tendency to daydream and often feel disconnected from their body energy.