I was in a similar situation a few weeks ago and it was pretty tense. I'm British, my wife Argentine. We got married early May then went on a two-week honeymoon to Europe. When I paid the overstay fine at Ezeiza on departure I was told straight that I wouldn't be allowed back into the country because it was my third overstay, but when I explained I'd just got married, I was told that in that case I would "probably" be ok if I showed the red libro de familia when I re-entered. But when I came back two weeks later proudly wielding my the little red book, the girl behind the window looked at it blankly and said something like "esto no me sierve para nada". I'd also booked a turno for migraciones online at the last minute to be extra safe, but the girl was seriously unimpressed by the fact that I'd booked it that same day shortly before boarding the flight from Madrid! In the end, she let me in purely because my wife, who'd gone through the Arg and Mercosur channel, came over to the window and got a bit emotional; So, yes, definitely appears to be up to the discretion of the immigration officer you meet on the day and whether they take pity on you/can be bothered doing whatever they'd have to do if they decided not to let you in.