Typically relay coils still work at 10V so well under the standard 12.6V a resting battery outputs, but it's best to test each relay with a bench PSU to see at what voltage it will not be able to trigger the relay (the voltage required to keep the relay triggered is less then what is required to trigger it).
As mentioned using a simple DPST switch is on one hand more secure but on the other you have to bring the (4) AWG 12 wires right up to your panel. While the starter wires are only loaded temporarily, the backup power will be loaded for the duration of the emergency (until you land). Not that a bigger deal, just more tefzel wiring and if done properly it should be fine (AWG 12 is enough to feed the 10A pumps and ECUs). Some voltage drop is expected (a charged lead acid battery "rests" at 12.6 (plateau) not at 13.8 (charge float limit) and the whole system should work fine until well under 12V (did not get a definite reply from engineers). Better turn off all unneeded avionics when in this situation and have a seperate backup battery or get avionics which have one already as optional.
As an additional note, if your battery is not able to toggle the relay coil, don't think it will be able to power the ECUs and power hungry pump (s). You must be certain to have a fit battery at all times, electronic injection system is built around a continuous power source hence the 2 Gens and Rotax's refusal of LiPoly or LiIon substitute batteries as these involve additonal charge cutoff and regulator electronics inside the battery itself which are an additional point of failure.
