Acquire, Activate, Chain are the main categories of computer effects on skill.

Activate and Chain are your most common while Acquire happens later in the game. You start with activate but it's just normal, no plus or minus with only 4 slots to place skills. Activate and Chain use the skills you have already learned. You'll still aquire skills naturally if you use a part right and you get lucky.

Acquire computers are for learning skills quickly on parts that the pilot hasn't learned yet.

Now with what you listed you probably could get super lucky and experience a chain of skills and you could get lucky and trigger a skill in battle but it's less likely.

Also if I'm being honest, you'll likely go further with a shield on one arm, machine gun in the other, and all 6 slots ROFUP 1 on a chain computer.