Yes, NSAID’s will hamper protein synthesis to a degree. However, I don’t think their impact is devastating if you’re just taking one recommended dose a couple of hours before an occasional workout (you mentioned pre in your post).
While just my opinion, I believe frequency is the prime consideration. Protein synthesis is a critical component of the anabolism process that takes place in the hours AND days following your workouts. Now, if you’re taking even the suggested doses at the suggested times (every 4-6 hours), then you’re suppressing protein synthesis for a much larger time frame. If you’re doing that for days/weeks at a time, then yes: NSAID use will very likely reduce your long-term muscle-building progress. You did not give the impression of taking these quantities, and I predict no "substantial harm" using the amounts and frequency I believe you're proposing.
You didn’t indicate why you’re taking them, either. Is it to work through a nagging body part, or do you sometimes suffer from minor headaches, etc.? If you’re trying to remedy a traumatized tendon or muscle, taking 200mg of Ibuprofen once every couple of days may not be all that beneficial.
Just don’t take some Advil to combat post-workout muscle soreness or something.
