I'm not familiar with that procedure but for comparison, IIRC a needle puncture to drain middle ear fluids (tympanicentesis) has healing time ranges from 4-7 days. I believe that a smaller gauge needle (25+ ?) is used as compared to tympanicentesis (20+ ?). One would expect that this helps improve the healing time but there may be other concerns as noted below.
I'm more concerned about your disease. Having Meniere's usually raises serious caution flags for an activity as dynamic as diving. But since it appears that you've already done some diving, I assume you've been cleared to do so and your condition has been controllable and stable. That is, until now. I assume your condition has changed because a procedure is being mentioned. I think that at a minimum, you'd first want to see how you respond to this new treatment before thinking of getting back in the water.
Next, I believe that a steroid (dexamethasone) is one of the injectable options. Steroids tend to impair wound healing. For one thing, this may slightly complicate healing from the procedure itself. For another, I have questions on the durability of the eardrum after repeated treatments.