I applied for a passport card about 1 1/2 years ago, nowhere near my passport book expiry. I don't remember the exact times and of course they could be different now, but I think I received my passport book back about 2 weeks after mailing it in and the passport card another 2 or 3 weeks after that. It has a 10 year expiry independent of the passport book.

As well as being a form of ID that doesn't have your address, I find that it looks official enough to pass for ID abroad (well, it is official federally-issued ID), even when you are in countries where you technically are supposed to carry your passport book with you at all times.