no
part of the extension review may include testing mobile
And if it doesn’t work they will fail the extension
There is no difference between hosted test and release.
Did you try their code calling your endpoint?
There is generally nothing special about fetch requests, and if it works on desktop it should work on mobile, UNLESS, read below
You may want to test your endpoint against https://www.ssllabs.com/ to see if you have specified a SSL configuration that is incompatible with Android