volt-ampere (VA) rating of UPS
No.

The VA rating expresses the maximum output power (apparent power S) that the UPS can provide:

$$
\langle S \rangle = \frac{V_{\mathrm {max}} I_{\mathrm {max}}}{2} = V_{\mathrm{rms}} \cdot I_{\mathrm{rms}}
$$

The apparent power is used only to choose output cable size, so it's not related to the UPS duration at all.
What you must seek for is the size of the batteries inside the UPS, that is measured in \$Ah\$, ampere time hours, dimensionally this number is a charge, coulomb.

ie:

PSU rated \$10Ah\$, your load needs 1A, theoretically the PSU can provide it for:
$$
\frac{10 Ah}{1A} = 10h
$$
ten hours. This assuming your batteries can fully empty and your PSU has unitary efficiency, that of course is not true. The manufacturer should provide some sort of "duration vs consumption" tables, and through them you can choose the PSU suitable for your needs.

Just choose your VA rating based on your load maximum consumption maybe adding a 10~20% of safety coefficient, then between the PSUs meeting this requirement choose one whose batteries are big enough.