I've run various releases of Tiny Core (11, 12, 15) from a USB pendrive without any problems.
One thing to note is that the eMMC Flash memory appears as mmcblk1 device. In the dmesg output:
mmcblk1: mmc1:0001 M62704 3.53 GiB mmcblk1: p1 p2 p3 p4 mmcblk1boot0: mmc1:0001 M62704 2.00 MiB mmcblk1boot1: mmc1:0001 M62704 2.00 MiB mmcblk1rpmb: mmc1:0001 M62704 512 KiB, chardev (239:0)
I did wonder about the rpmb. Google tells me:
RPMB is a self-contained security protocol with its own command opcodes and data structures. The mechanism for this protocol involves a shared key and a HMAC (Hash Massage Authentication Code), which is used to sign all the read/write operations accessing the secured area.This is something I haven't explored.