I would say not. Outside of checks I’ve never been asked for my licence but Sod’s Law applies. My experience of licence changeover with IAA has been very good. Although the licence generation process was painfully slow, once I could send mine in the turnaround was very quick. Suggest don’t use Post Office - too slow. I don’t know how your roster looks but maybe choose the longest gap and hope it gets back in time. Recommend a proper courier with guaranteed delivery time (the yellow and red machine should do an overnight service).
If the licence doesn’t get back before your next duty you should probably ring in and explain that you don’t have current licence or if you feel you have reasonable managers have the discussion in advance and agree on a strategy.
Good luck