Can an rMBP work via MagSafe even if the battery is discharged?

Hi,
I'm going to buy an rMBP (13 inches, late 2013). When I tried to buy it last time, it came to me discharged, and shut down in a couple of minutes even though by that moment it had been empowered by a MagSafe.
I think, such a computer is defective. It's a complicated story, though and I'm not giving details cause I'm afraid, that the story would make this post too long.
Now, must any rMBP work without shutting down if it has been switched on with the help of its corresponding MagSafe?
There’s opinion that if the battery is completely discharged, the Macbook can't work after 5 minutes because of special protection which cares for lithium. But why? The previous models can work with discharged accumulators as soon as they’re plugged in to a socket. Moreover, they can work without accumulators at all.
Nick.

If you charge it for even a short time, say 15 minutes, before switching on; then it should work normally. If not, walk away. All I've seen work from the adaptor regardless of battery charge.

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