Assuming that the external supply has sufficient current and power capability the only reason I know that the Seestar will stop working is when the internal battery fails. A supply with 3A and 15W should be more than sufficient since the Seestar only draws 4W while tracking and imaging with bursts up to 7-8W when slewing to a new target or closing the arm. Do the math, the internal battery is rated at 22.2Wh but in tests it takes about 26Wh to fully charge from 0% SOC to 100% SOC (may be slight variations from battery to battery). Hence the 6 hour estimated run time (26Wh/4W =6.5hrs). Add another 0.5W for the dew heater. Also if you do a fast slew I have measured 10-11W so 15W should be more than enough external power to avoid tapping into power from the internal battery.
Now, it is true that lithium ion batteries do not like to remain at either 100% or 0% SOC. In the former case that puts stress on the anode and in the latter stress on the cathode. This can cause cracking and delamination which ultimately leads to loss of lithium capacity (LLC) as it is termed in the technical literature. But, as Seestar Support says it will be small and will take a long time to degrade the battery significantly. The internal battery can be replaced very easily and I see that Agena Astro finally has the replacement batteries available. You could avoid degrading the internal battery life by discharging it to 60% SOC in between sessions and then charge it back up to 100% SOC before your nightly session with the external source if that is possible but I think it may not be worth the trouble.. When using an external AC-USB source to power the Seestar with the internal battery fully charged before your session you can now operated below the -10C discharge spec for the internal battery without worry since the internal battery won't discharge. Now, you may still have to worry about other internal components at too low of temperatures but that is a different matter.
Best Regards,
Curtis