Yes, for the IBM 360/30 at least the 16 32-bit registers (and 4 64-bit floating-point registers) were stored in the same core memory as the main memory.
The IBM 360/30 used the IBM 2030 Processing Unit as it's CPU, and the IBM 2030 Processing Unit Field Theory of Operation manual states on the page 1-4 that "The sixteen general registers and the four floating point registers are in local storage." On page 2-72 it states:
Included in the 8,192-position storage unit is
an additional 512-position auxiliary
storage section. In this section, 256
positions are reserved for use by the miltiplexor [sic]
channel. The other 256 positions
of local storage are used by the CPU for
special and general purpose registers
Similar statements are made for the 16K and 32K storage units. These storage units use core memory. On page 3-10 you can see how the the registers are laid out in local memory.
The IBM 2030 is basically an 8-bit CPU that executes microcode that actually executes the 32-bit IBM 360 instruction set. It has internal 8-bit registers that I assume are implemented with semiconductor logic, but IBM 360's architectural registers are stored in core memory alongside the main memory.