Well, I can confirm that installation of TC to a USB stick from inside a VBox VM (booted in my case with 'tinycore_3.7.1.iso', followed by a download of 'install.gz' and loading of the same via the System Panel 'Load Starter Pack') is feasible.
I just did a test with running tc-install and installed TC in an EXT2 file system on the entire device. My only problem was that I needed two attempts for the USB stick to be fully available inside the VM. Inbetween both attempts I installed the extension pack (for USB 2.0 support, which is probably not mandatory) and required a (proper) restart of VirtualBox after the USB driver installation on the host (i.e. WinXP in my case), which occured after I assigned the USB stick to the TC VM the first time around.
So this is not just a theoretical option, but might not be made easy due to USB device issues between the host OS and VBox.