Not sure why this should be a problem as long a the CC is able to keep the battery voltage below its maximum rating and above LBCO voltage ?
I suppose if the AC loads change too much, the CC and solar cannot keep the AC output regulation steady, you might run into problems but it shouldn't hurt the inverter ? It isn't like this hasn't been done before. Just have to make sure the battery voltage is within a range and battery ripple current isn't so high that it ages the capacitors too fast.
But how do you think a hybrid inverter--solar controller works ?..... Except those usually run the solar output voltage at the inverter link rail voltage (hundreds of volts). They still have ripple current but it is lower than at say, 48V.
Having said this, it is definitely better to use batteries.