TMS320F28379D: Can a CLA R/W directly to the register of the CLB?

Yes the CLA has access to the CLB on F28379D. You also have the option to send data through shared memory to CPU, then use CPU to communicate to the CLA.

CLB1/2/3/4 and ePWM1/2/3/4 are tightly connected on the F2837x devices. For example to assign CLB1 to CPU2, you will assign ePWM1 to CPU2.