MCP2551 to monitor CAN activity without processor
Technically, yes, it is possible.

But it would take very fast processor to even store raw network traffic, yet alone analyze ("monitor") it. Keep in mind that CAN bitstream cannot be decoded without huge efforts if it does not contain timing information (frame boundaries), so it either has to be processed in real time or you need to insert time-stamps into it.

Letting CAN controller do all this heavy lifting and processing parsed messages is much easier. This is exactly how all network sniffers I know of work.