Yep, using the SD socket breakout board and resistor voltage dividers should allow you to talk to the SD card using the SDFat library.
If you have an old dead device (camera, printer, etc) with an SD socket you can pop it off the circuit board and just wire directly to the socket instead of buying the socket on a breakout board. The easy way to get the socket off a board is to heat the other side of the board with a torch. When the solder melts, whacking the board on a hard surface should cause the socket to pop right off.
If you get a Micro-SD card with an SD adapter you can solder wires to the adapter pins an use it as a Micro-SD socket.
Ya that works great, the pins on a card adapter also just barely line up with a .1" pin header, so you could also mate it with a click lock shroud, or directly to a male header strip and have it breadboardable.