The short answer to this is no, TechWARU cannot be used on write-protected flash drives.
The slightly longer explanation centers around TechWARU's run-time. TechWARU, while it is running, will attempt to save a lot of data in two places, the registry, and the Assets folder. The latter includes downloaded portable applications, temporary files, recovery files (tremendously important considering TechWARU works on broken machines), and preference files.
Clearly, write-protected drives would prevent these files from being written and thus cause TechWARU to crash.
The quick solution to this is to copy TechWARU and it's Assets folder to the Desktop of the infected computer. Copying vs moving those two will keep a working copy available on the drive while allowing TechWARU to write the previously mentioned files.
A quick note: If TechWARU can't upload reports due to network issues or some other reason, moving the Assets folder from the Desktop back to the flash drive would allow you to run TechWARU on a working machine later and upload the reports for the work done on the previous computer.