TN8703

If this is the inverter, it states 30V to 115V is the MPPT range, thus if the complete panel is in full sunlight, it would produce, but, a 380W panels is likely only able to produce just above 300W and the inverter, possibly consuming anywhere up to 100W itself, is the potentially 200W production for a few hours a day worth the effort/money invested?

I would say that inverter would perhaps only use 25W for self consumption. 100W is even more than what a 8kw Sunsynk would use.
Without guessing. I have used a 200W flat on a car port getting only sun up to 14h00. This panel could provide a bit more per day than the self consumption. To increase the charge power just keep the grid off and only switch on during LS. This way only the display uses power and not the inverting side. As has been said the whole panel must be in the sun. The 380W will for sure work as long as the expectation is not to get 380W x 5 hours into the battery.  If 2 x 20Ah would store enough for your use go ahead. As indicated on less than 5hrs sunlight a day very little power available for storage above the self use.
When I had only the 200W panel it was OK for my back up as my main PV is grid tied. The back up worked fine for all my lights and WiFi and laptop when needed.
A good idea to get the bigger inverter for future use.

Also your batteries are tiny for such an inverter

I also had the same problem, unless we stage 18 and any drop helps I also concluded it is unfortunately a waste of time and currently the trustees wont allow it anyways.
I also noticed the summer sun doesn't hit the spot like the winter sun does and the location is just really non-ideal

So I have been wanting to do something similar at my place but it's not that practical. If your balcony is east or west facing, you won't really get enough sunlight to make it worth doing. If you already have the panel, might as well put it up. Otherwise, if you are buying the panel, keep expectations low as it will take quite some time to for the panel to pay itself off.

What is the Vmp? that's the more important figure in your question, if Vmp is above the MPPT start up Voltage, then it should work, but be aware, the whole panel should be in sunlight and not only a portion of it, else all bets are off.

It will work, it may just be marginal when there is no full sunlight.

Looking at the claimed figures for that Inverter, it could work but will be very restricted if any cloudy patches come over as the Panel voltage just exceeds the minimum start up voltage of the MPPT. MPP Range @ Operating Voltage 30 ~ 115VDC
Perhaps you should consider spending a bit more on a larger panel, i.e. 550 to 600W range that provides around 50VoC.