Does Amp Hour Rating Take Into Account Voltage Drop Relative to State of Charge?
If an amp-hour rating is accompanied by a description of test conditions,
then yes, one of those conditions is the voltage at end-of-capacity,
i.e. the discharge voltage drop.

An amp-hour rating which is not accompanied by a description of test conditions
is best treated as a bit of enthusiastic sales-speak.   Unless the 'backup
power system' is coincidentally similar to a documented battery test, your own test results will have to wait until you actually purchase batteries.
The results depend on your power system control  electronics,
after all.

On a lighter note, some clock batteries in my experience had exactly the
lifetime at load that the manufacturer's amp-hour rating predicted!