well I would do it but here's the bad parts.
home recivers are 8 ohms and normal car speakers are 4! So this would tax the amplifier on the home audio and upon louder volume posssibly toasting it. But unlikly with small 6X9's and 5.25" so lets forget that..
DC>AC>DC power +adding another power hungry car amp for the sub!..As soon as the subs bass kicks the inverter is gonna kick off from low juice which will now turn the home theatre off. That can be corrected with Cap's, better batteries but you see the price of those hightech batteries $180...WOW
I have spare 5.1 Home theatre reciever with Toslink and inverter. So I will hook this up in the next few days and compare it to SB X-fi 5.1, I'll post my results
Im bored so why not I suppose