I believe you are asking about the case where one UPS in plugged into itself, and with a (fully) charged battery.
I'm not sure of the result, but I believe there is a chance for the UPS to fail (i.e. not work as intended) or develop a permanent or temporary fault (i.e. component failure / bad parts).
The problem comes from the fact that the UPS in placed into an inverting feedback loop, that is not consistent with its design for intended usage. When you turn the UPS on, after it has been plugged into itself, the UPS detects no AC from its input (the plug), so it switches to deliver power from its batteries. This causes AC to be delivered to its output (power sockets), which triggers the UPS to switch back to "mains" power mode of delivering power from its input (plug). This halts the power being sent from the batteries, and thus no further power is sent to the plug.
This could restart the this pattern ad infinity until the UPS controller determines it is not operating as intended and powers itself off (in some "smarter" models) until manually powered back on, or failure. Depending on the speed of the cycling of switching to batteries and back to the plug as the power source, various components could fail. As an UPS contains essentially back-to-back SMPS (AC to DC, and DC to AC) that have high voltage stages depending on design, these high voltages (~400-800 V) are high enough to generate a significant spark that could cause a fire.
The best case outcome is that it cycles back and forth several times rapidly and powers itself off.
I have had too many UPSes fail from harsh (outside of intended or specified usage) real-worth conditions - excess loading, bad AC voltage levels from the AC mains (wall socket), not testing and replacing batteries, that I doubt that many, if any at all, UPSes could reliable withstand such abuse.