What's plugged INTO the RPS?

If the RPS isn't actively providing power to the switch, the RPS isn't drawing much power whatsoever. (I can't provide you with exact numbers, sorry.)

The 675W maximum is how much it can drive to the connected switches.

If a switch consumes 45W (a 3560-48TS), it's not magically consuming 90W by being hooked to an RPS- instead, it's drawing 45W off its primary power source, and 0 W off the RPS. (maybe a few W.)

When it fails over to RPS, now the switch is drawing 0 from the primary feed, and 45W from the RPS.

Total load has stayed ~45, now it's just come from different sources.

[This is different than a chassis based switch, which I believe shares load between the installed power supplies- I understand the RPS to be an all or nothing situation.)

If your RPS is on a different circuit than your switches (as is probably best practice), I'd calculate peak consumption of the RPS as that of all connected switches + a few W worth of overhead just to keep the RPS at a steady state- I'm imagining this to be ... I dunno, 20-40 W? I think that's going to be high, but this illustrates that even if your RPS is at full offered load, it's probably not going to hit 675W... unless the downstream switches are doing PoE. But you'll need to understand how much power the downstream switches are consuming, and that's the basis of your math.

Cisco isn't very good about presenting "steady state" information on RPS units, considering that they're not drawing much power unless they're under load.