logic cells: easy, by universality of NAND.
RAM: distinction between flip flops and RAM is unnecessary from a strictly technical standpoint. a massive (or not so much) array of flip flops with decoder and mux (also just made of NANDs) can get you by.
ROM/flash: maybe I could argue NAND flash counts as just a NAND gate, but not quite. I'll concede nonvolatile memory with just plain old NANDs. May I suggest a https://en.wikipedia.org/wiki/Diode_matrix?
"analog components": having Vcc and ground available is an implicit requirement of having a functional NAND gate, and IO could just be some wires mirroring a memory location.
Overall I'd say its a largely accurate statement. All you need is something to set up your initial conditions (e.g. program in memory).