Hmm,
I think I see what you are driving at, having read your previous thread. You don't want to start the car, only power some accessory circuits. There is a solar battery charger that trickle charges a battery through the lighter circuit on cars that have the lighter circuit on continuous power. In a similar manner, you should be able to get sufficient power to circuits through that connection, even if it is switched. The only problem will come if the wiring relies on a completed circuit through the battery, which in your case is toast. It can't hurt to try. Even if you try to draw more current than that circuit is capable of handling, you will just blow the fuse. Disconnect some other fuses for circuits you don't need until your draw drops if that happens.