No, the BIOS cannot work without the CPU.
The very first thing your computer does when you power it on is checks that the connections between the CPU and RAM are good. This is a simple electrical check that all the bus line outputs are connected to the correct inputs. If this simple check doesn't pass, you get a beep code (or possibly an LED display on some motherboards). This check does not require the CPU, however without the CPU present, you may not even get beep codes, as even that requires some measure of processing (depends on the motherboard).
Once these things check out, however, then the CPU begins execution of the program contained within BIOS ROM that performs some additional higher-level checks (such as whether memory timings work, whether additional firmware for onboard devices can be loaded correctly, etc). This ROM program is written in x86 assembly language and does require the CPU to execute it.
What happened in your case is that the CPU is electrically compatible with the motherboard and does work, but lacks some low-level feature support that the motherboard depends on. Perhaps you used a CPU that has a higher TDP (generates more heat) than the motherboard can handle, has more cores than the BIOS knows how to initialize, or possibly doesn't support some power state the BIOS is trying to set. You didn't mention what CPU/motherboard combo you're using.
In whatever case, though, the CPU is providing enough support to the BIOS that it can execute the programs stored in its ROM (including moving bytes in and out of video memory). It just can't get further than that.
It's probably just checking the family and stepping IDs from the processor against an internal list of supported CPU types. In many cases, this can be patched with a BIOS upgrade. But you'd need to insert a supported CPU first in order to flash it.