...The fact that the scope hangs when a USB to serial interface is connected, probably has to do with the boot loader. I have seen this happen on a Lichee nano too, when I was playing around with linux on a F1C100s. Not sure why this happens. Was in the time I was starting with the reverse engineering of the FNIRSI-1013D. Did not investigate it further since the FNIRSI scope does not use linux.
But good to know this, because I was thinking of integrating a CH340 USB to serial module in the scope, but if it would need to be connected to a PC to allow the scope to start is not what one wants
Just in case my memory was teasing me, I've just checked and it effectively hangs if powered on with the serial to USB not connected to the PC
I've also verified that if you connect it to the PC with the scope "hanged", the dialog that appears is the same that when you hit a key at the beginning of the boot procedure to stop it (see attached images, first one connecting USB after powering the scope and the second one keeping a key pressed during boot) so yes, it's the boot procedure that stops when USB is not connected (apparently this is equivalent to hit a key...).
Finally, this also may happen because the CH341A in my adapter is powered from the USB, not from the scope. I'll make an experiment on this and report back.
EDIT: Done! Tried powering up the scope with the CH314A connected to TX, RX
and 3.3V but not to the PC and it didn't hang. I tested it three times because in one of the tests it also booted OK without 3.3V... maybe some loose connection or something, but most times it hangs on boot when TX and RX are connected to unpowered CH341. So maybe you can integrate the module into the scope as long as it's powered from the scope. I don't know if this will bring new problems when connecting USB to the PC with the scope on (of course, the module would have to be modified, removing the 5V to 3.3V regulator, for example)
EDIT 2: The CH341A module I'm using is the one known as "CH341A Mini Programmer (Black Edition)",
modified for 3.3V interface