The market will correct very quickly, as competitors will immediately head over to McDonalds to purchase $\infty$ burgers at $0, killing MCD dead in seconds.
The moment McDonalds applies a purchase limit (Free burgers! Limit 5 per customer), the burgers have non-zero cost, as they require a person's time in order to purchase.
If McDonalds does have enough capital to buy long-term customers and kill off competition with free burgers, perhaps they should consider it. I assume that they've considered such a strategy on occasion and concluded that it isn't worth it. Burgers are probably worth more than $0 to McDonalds, too.