@Tommy-D, any verb tense can apply in the appropriate context, even if not all are equally common. If any exception exists, I cannot think of one at the moment.
For ir + a + infinitive, I wouldn’t typically use it for an action that has just started, but to describe how an ongoing action (movement, more specifically, as implied by the verb ir) is being performed. Some examples:
Olha o condutor do carro. Ele vai a dançar! (Look at the car driver. He’s dancing!) - moving with the car
Eles foram a conversar durante todo o voo. (They chatted the whole flight.) - moving with the plane
The same can apply to vir + a + infinitive when referring to incoming movements, but your general description is still accurate for the more subjective use of that structure.