Transistor count of a shift register
No, a shift register needs more transistors per bit because you need master-slave behavior like an edge-triggered flip-flop. In CMOS you can make a decent flip-flop with about 18 transistors: an inverter for the clock, four inverters for the latches, and four transmission gates for the latches.

You could pull the clock inverter out the flip-flops and go to a 2-phase design. If you need the register outputs to drive anything other than the next bit in the register then you might need a few transistors for a buffer in each bit. If you don't care about noise immunity and speed you could save a few transistors by using a single pass transistor instead of a full transmission gate.

For estimations, I would assume 24 transistors per bit.