What are the chances of, if at all, resuming peritoneal dialysis after having a laparoscopic cholecystectomy?

Safe to resume! It is common practice to hold PD post op for a day or so (if no urgency with normal potassium, no fluid overload, etc exist), then start low volume exchanges (0.5-1L) , 3-4 times daily and then go back to high volume regular exchange regimen in 72 hrs or so. .
Good. Once you have healed from your surgery you should be able to resume peritoneal dialysis. There are usually very few adhesions after laparoscopic cholecystectomy that would interfere with peritoneal dialysis.
Lap chole. Resuming PD after a lap cholecystectomy is easier compared to an open chole. Experience with this is essential. Typically, after a lap chole, it is important to lavage the abdomen with PD fluid each day to clear out blood and debris, but one cannot leave fluid in the belly until about 10-14 days pass. Then one resumes PD with lower fill volumes and gradually raise fill volumes over several days.