Never head that one..
Not involved with/researched 'conversion' or validation ('convalidacion' in Spanish) in the past. I only did full Argentine PPL. True, to fly in Argentine airspace, you need to have some aviation Spanish. Even officially uncontrolled airport may have A/G radio that may sound like ATC, haha. The difference is in couple key words in 'clearance' etc.
With the bureacracy of ANAC and inflexibility of clubs/schools, you're not likely to sort it pain-free without more than simple check out that you're safe. It's not customary to rent aircraft to visitors. Previous posts I read about Argentina before spending summer (well, their winter) there, suggested it wouldn't be easy/doable.
As suggested, 'renting' 4 seater with local experienced pilot would be easiest. They do radio and take off, you do most of the rest.
BTW, air law is fairly easy for PPL level.
Yeah, unless people ask for nationality for paperwork, it may be safer to say you're Irish etc. To save some awkward time. Lots of older club pilots or some career instructors (not many of those in Argentina) served in military.
Stuff mentioned in this
suicide thread on pprune from 2010 doesn't help things either.