From the Tinycore website FAQ:
What are the minimum requirements?
An absolute minimum of RAM is 46mb. TC won't boot with anything less, no matter how many terabytes of swap you have.
Microcore runs with 28mb of ram.
The minimum cpu is i486DX (486 with a math processor).
So the simple answer is no.
It is possible to fit a stripped down kernel, uclib, and busybox on a floppy. I don't know if it could
boot in 4Meg of RAM though. Even if it could, there's not much you could do with it.