Not sure how you count the 24 bits you want to transmit, but if this is the sum of the 8-bit control word and a 16-bit data filed, then the answer is yes, it will work.
The data size field (DSS) in CR0 determines the width of the data field only. The control word is always 8 bits wide.
If you set DSS to 16 bits, then writing any value to the transmit FIFO will trigger a complete microwire frame transfer: The LSB of the data written to the TX FIFO is sent as the control word, followed by a dummy clock cycle, followed by 16 clock cycles used to read the data field.
While SSEL is pulsed low by hardware for the duration of the sequence described above, you are free to drive your own GPIO version of a slave select if you like.