I do this all the time with no problems or discernible difference between the quickly processed paper and the later processed paper.
I typically have time to print 2-4 negatives in a session to the point of my best effort. If I have a negative worth printing/framing then I usually make 5-10 copies of the print. Once I have the printing sequence down, I expose the copies and put them in a paper safe. By then end of the session I have 10-20 sheets to process. Most of the time I process the same day, sometimes the next day. On some occasions up to 3 months later (Kentmere FinePrint VC FB). I never have any problems and the processing sequence and toning is much more time efficient when done in batches.
I don't think the process degrades quality at all. For me, it improves quality because when my mind is in printing mode I am not distracted by the monotony of processing.