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
(Figure 2-74).
(Emphasis mine)

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.