I am aware of this question regarding feats that can be used when firing a ranged siege engine and this question regarding whether Vital Strike can be used when firing slow-firing weapons. The answers to the first question do not discuss Vital Strike, while it is unclear whether the answers to the second question apply. I believe that the essence of this question boils down to:
- Is firing a light ballista an Attack action?
- Is there any other reason that a character firing a light ballista cannot use this feat to turn base damage of 3d8 into 6d8?
Regarding the first sub-question, I found it difficult to find any clear statements regarding what type of action is required to fire a siege engine. The best indication I could find was in an example on page 19 of the Players Guide to the Skull and Shackles Adventure Path (emphasis mine):
...If the same light catapult were instead crewed by three creatures, two could spend full-round actions aiming it and the remaining creature could fire it with a standard action.
If anyone is interested in the context, the character hoping to use the feat is an 8th level ranger with the Siege Engineer and Deadly Aim feats, employed as light ballista gunner on a pirate vessel. (I am already aware from the answers to this question that Deadly Aim and Vital Strike can be used in combination.)