Does adding 1X PBS (phosphate buffered saline) change the pH of an acidic solution like HCl?

The pH of PBS is 7.4, which makes it slightly basic. 1M HCl solution has the pH of 1. While it's true that adding a base to an acid will change the pH of the acid, unless you use a very dilute sample of HCl and a very large sample of PBS you will need a very sensitive pH meter to see any pH change.