Just want to make sure I am reading this right.

 When I make a strength check, I can use a charge to add a bonus equal to my int bonus.

Senerio. (for ease,) my character has a str of 20 and an Int of 20, each gives  a bonus of 5. I am attempting to grapple a foe

I grapple my foe and we roll, let's say I roll a 15. I then add my +5 from str. Then I burn a charge of the armor and add my +5 from int. With a result of 25 strength check. 

 No were in the the armor disruption does it say it replaces the strength bonus/ used instead of (ala battlesmith sub class ability). It's not using two attribute on the same roll because it's the armors ability, which just happens to be equal to the int. 

Am I correct in this? 

You're right, the Intelligence bonus is in addition to any other bonuses you can apply, so if you're also proficient in Athletics (since it's a Grapple) and your proficiency bonus is +4 you would have 29 on that check. 😉

This is somewhat balanced out by having to decide if you want to add the extra bonus before you roll the check/save since the bonus is applied to "the roll" rather than "the result".

Quote from Stoutstein >>

The rules for any roll modifier that doesn't have a specifically listed timing is that it is added after the roll but before the outcome is known. It's easy to remember this if you view rolling the D20 as the initial step in "making" the check,save, or attack which isn't concluded until the outcome is determined. The game has PC faced sequences not players. 

Is that actually a general rule specified somewhere? Usually effects that can be added after seeing the roll explicitly say "you may use this after rolling but before you know the result" or similar, which this does not, though I can see how it might be vague enough to allow that.

It still means you can't turn a known failure into a success though, only a potential one (since you usually don't know the DC you're trying to beat).