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Many years ago I hypothesized that foamed metal with a high pressure inside the cells might be useful as a strong but lightweight building material.

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You don't need the high pressure. Metal foams are currently used in cases where energy absorption under stress is essential, in theory they could be used for many structural uses but they are still pretty expensive. (In one of my favorite sci-fi novels, metal foams from asteroidal material are used to make super-high skyscrapers in NYC http://sff180.com/reviews/h/haldeman/worlds.html) Might make really good tank armor too, you could make vehicles that just a little heavier than infantry fighting vehicles but are as tough as a M1 Abrams.

Question: does the ability to absorb energy necessarily means that any deformation will be permanent, or do metal foams that absorb energy get back to a preferable shape, like a memory foam mattress?

It is usually permanent. See the article.

I seem to recall aerodynamically self-stabilising chunks of metal foam being dropped from an asteroid into the sea for recovery in an earlier Peter F. Hamilton book (you know it's early because, while there is, as always, a mega-billionaire, she didn't have a harem).

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