You might want to have a look at this:
yes they can but the only caveat is that i would put the GTI on a separate breaker then the one the UPS is on, in case it leaks voltage back into the grid when operating . that way if the breaker turned off on the UPS and their no sources that draws the leak volt to zero on the grid side the GTI will not try to start ( as I mention this happen to me once and burnt my GTI) or you could put in a drop relay if no AC it drops AC connection to the grid for the GTI isolating it from the UPS
Thank you both for your advice. I’ll spend the remaining weekend thinking on it. 
Well, I understood UL1741 requirements and I tried to comply that safety rule using an automatic “CB” at L2 entrance to avoid injecting UPS power into the island. The proposed SSR is to be controlled by L1 so as to keep power within home only.
My only concern is when the grid gets back. Most probably than not the pair GTI+UPS will be dancing together but not on the same rhythm of the grid… some feet may be hurt!
if I understand your drawing --you could not run like that USP would have to separate from your lines your ups would burn out in minutes. as a UPS is designed to power stabilize so if your power browns or surges for some reason the UPS kicks on to stabilize it but the line will be active and out of sync with your UPS ( as most UPS are modified sine) and it will hammer ( a very loud pulsing hum) and burn out
if you want to run like you drew above it would have to look like this
by the way to start a fridge you would need an inverter in the 1.5 kw range or higher. a UPS unless it is designed for fridges starts will not work as they are not generally designed for that. just like you are not suppose to put a laser printer on a UPS they kill them in no time
Indeed. The inrush current of a normal fridge compressor motor will be huge in comparison with the running current - easily 10 times, probably more. This shows my fridge starting (on top of a quiescent load of about 40 W). The 10 s average power is about 2½ times the running power.
Thanks for taking your time, @stephen. Did you notice it is a 2-phase (L1+L2 120° apart)? I wondered if I connect (true pure sine wave, not a modified one) UPS’ input and output to different phases it could avoid the scenario you described. Of course the UPS must be of “battery+inverter always on” type, otherwise with power present it would bypass them and short two out of phase lines on.
I’m aware of the fridge start surge restriction, @Robert.Wall, it requires a BIG UPS indeed, and they are not cheap.
My original intention was to keep the solar inverter on to take advantage of uninterrupted power. So solar inverter should be connected to the inner branch of 3-poled (4-poled for 2-phases). Just moving GTI to the right of the figure instead of left, to keep it on the circuit but insulated from the grid should do, I think.
P.S.: I know UPS has its own battery charger but an external one is required to charge the external bank, that is much above internal charger capacity. UPS internal batteries are usually designed to provide just enough time to orderly shut down computers. If you want them to stay more than a dozen minutes on you has to extend battery capacity.
to my knowledge UPS are not that smart. perhaps there are some that are, that will sync to the grid otherwise they are very basic device with upper and lower limits. if one of the triggering requirement is met it triggers a 3pole relay with in them that switched from the grid power feed to the internal inverter. once the input AC voltage stabilizes and falls within norms it switches back to line power…
I think this would be the best route it the simplest and safest → transfer switch
then just get a 24 volt charge controller and inverter
and 24 volt battery back
either wire the charge controller to you panels or to a power supply to charge you batteries