I assume you mean "In Circuit Emulator"

Yes and no.

There are 2 types of ICEs bondout (e.g. Nohau) and non-bondout (e.g. Ceibo)

The bondout type of ICE uses a special version of the chip that has been modified to allow "poking" inside the chip without affecting operation.

The non-bondout ICE will, indeed, use some resources. Ceibo, for instance uses the memory area 63k-64k and 4 bytes on the stack.
A breakpoint is achieved by replacing the instruction(s) at the breakpoint with a call to a routine in that added code which effectively shut down the processor, communicates via shared memory with another processor on the board, that processor then communicates with the PC. When the "continue" is clicked on the PC, the "extra" uC communicates to the emulating uC which then execute the replaced instructions and restores everything and then return to your code.

While the bondout emulator does have some advantages such as non-intrusive trace it has two disadvantages: You can not replace the chip with whatever derivative you work with next (YOU can not buy a bondout) and they are very expensive.

If you, after this novel, have specific questions, do post them.

It is better to emulate fun than to simulate it, but best of all it is to have fun,

Erik