An exchange is 100% necessary. Bootstrapping from an existing currency is only one way of getting bitcoins into an economy. Admittedly it's the easiest -- but perhaps "easiest" becomes a less accurate term in less free countries like Argentina.
If Argentinians started earning bitcoins directly, then no exchange would be necessary. The exchange would not be for dollars, but would be for "goods and services". The hardest part is finding something that some foreign owner of bitcoins wants to buy. However, it could also be that a foreign owner of dollars, who is already buying from Argentina can be persuaded to settle bills in bitcoin.
Without that bootstrapping there's little you can do there. The current government restricts not just the purchase of foreign currencies and precious metals, but also imports.
I'm talking about exports though. People in Argentina selling goods and services to foreigners is exporting. I'd very surprised if cash-strapped Argentina banned exports.
For mining, you need equipment that effectively is a lot more expensive than elsewhere, you cannot easily import mining equipment. If they decided to start buying and selling products and services they'd be very strictly limited to services since they cannot reliably buy outside.
Argentina must export more than fossil fuels? What about the agricultural sector? But services too would be possible.
Maybe web designers, programmers, etc can offer their services directly in BTC and then use it for complementary services, as a complement to their main salary typically in AR$/US$. It's limited, but it's something.
Exchange rates sort everything out. If only people could be persuaded to use bitcoins within Argentina, then the demand within Argentina would rise, and the few that were entering the country via service providers/farmers would be enough to run an economy (remember there are eight decimal places of divisibility). The more valuable BTC became within Argentina, the more attractive the export business would become.
The ARS/BTC rate would sky rocket, just as the ARS/USD rate is going/has done anyway. At some point, ARS would only be useful for paying taxes, but you'd be able to buy so many for a few BTC that it wouldn't matter in the slightest. Importantly: BTC would allow a capital-control free existence. The stupidity of the government wouldn't be passed on to the people, rather the stupidity of the government would be visited on the government.