That is a very good question. I would think it takes long term ongoing usage, but I also think the smartest thing would be to consult a pharmacist or doctor. Perhaps, if your thought is correct, then how one’s muscle development naturally occurs would also affect the success of the anti-inflammatories.
Now I am curious, so, if you fail to find an answer here, but do learn something later, will you post your findings?

Yes, there does seem to be some impact on muscle recovery:

“Long-term usage (more than 1–2 days) of NSAIDs [non-steroidal anti-inflammatory drugs] is widely believed to be counterproductive for muscle recovery, as inflammation is an integral part of the recovery process. However, all current research suggests that upon the passage of two or more weeks, muscle recovery will be the same, whether the subject uses NSAIDs or not. One may safely conclude that NSAIDs can be used as a short-term measure (1–2 days) to alleviate pain and soreness, but after this the patient should rely on more traditional recovery methods (protein consumption, restful sleep and rehabilitation exercises of the muscle).” (source)

@thorninmud Makes sense, thanks!