I am unaware of any studies on the use of anti-inflammatory drugs in conjunction with coolsculpting. Given the basic science though I would doubt that you would kill all of the efficacy of the treatment by taking a drug like celebrex.
Celebrex or Etodolac post coolsculpting
Celebrex or Etodolac are generally not needed post coolsculpting treatment. I would consult with the physician that treated you prior to taking either as he or she understands the scope of the treatment and your medical condition and history.
The treatment consists of freezing then the massage afterwards. There is a study that shows improved results with massage so that should be done. In terms of anti-inflammatories there is not a study I am aware of at this time.
Coolsculpting and anti-inflammatory drugs
Coolsculpting is an excellent procedure and should not be affected by drugs like Celebrex. Please consult a board certified physician with experience with Coolsculpting for the best results.