Well, i took Rome in my Russian campaign (they are Orthodoxes too), thus depriving Papal States of their last land - and nothing happened... well, except that Denmark declared war some five turns after... but I'm not sure it happened because of this take-over.
By the way I had to kill two or three (cannot recall precisely) Popes prior to taking Rome - also never had seen "relation worsened" with any other European state (except Papal States, of course). Also after capture of Constantinopol just Sicily and Milan declared war agaist me - so it wasn't such nightmare as i thought (after reading some posts of players who managed to do the same). Campaign setting were VH/vh btw...