Scenario: Diesel van, sitting in below freezing temps, needs plugged in for at least an hour or so before starting to get block warmed up for easier starting. Would it be possible to run an extention cord in to your house bank to warm the block. How many batteries would you need hooked up to warm the block before draining those batteries.
Short answer - Bad idea, high cost, don't do it.
Anything down to about 4° F and glow plugs should be all that's needed if you have treated fuel. Engine block heaters are generally in the 1000 Watt range, though they can be as low as 400 Watts (generally more for an oil pan heater) or 1800 Watts for extreme temperatures. But for a 1000 Watt heater, it'll draw 8.33 amps at 120 volts AC, which converts to 92 amps at 12 volts DC, including the 10% loss for the inverter.
A 92 amp draw is a very high amp draw off a battery bank. It's bad enough when it's a microwave that's in use for 5 or 10 minutes a day, but it's brutal when used for an hour or five (it'll be at least one hour or two hours to properly warm the engine, with four or five being what is really needed for below zero temps). But assuming only one hour and not a minute more, that 92 amp draw becomes considerably higher with the Peukert Effect figured in, depending on the battery bank size.
Also, there's the factor of whether the batteries are marine "deep cycle" hybrids, like the Walmart batteries, which are absolutely not suited to very high amp draws of even a few minutes, or if they are true deep cycle batteries like Trojan wet cells or AGM batteries.
If the 125 amp hour hybrid Walmart batteries (Everstart Maxx) are used, you'll need at a minimum of three of them, for 375 amp hours. A 92 amp draw from a 375 amp hour battery bank becomes a 136.93 amp draw due to the Peukert Effect. From a 500 amp hour bank (four batteries) 92 amps become 127.42 amps. (even a 1000 amp hour bank, and 92 amps becomes a 107.15 amp draw). So you can see these are significant amp draws, and they will kill a hybrid battery's thinner lead plates after just a few uses. They likelihood of three of these batteries lasting an entire winter is slim.
If you use true deep cycle batteries which can actually handle the high amp draws required, the batteries will last, assuming they are properly and fully recharged after each use, the Peukert Effect still makes the amp draws the same brutal draws.
It's just not cost effective at all. You'll have to spend between $400 and $600 on batteries and connecting hardware, rather than spending a fraction of that on 200 feet of extension cord. For that matter, a cheap generator is far more cost effective, and more energy efficient.
Batteries are not a good option at all for any kind of resistive heat application for extended periods, longer than a few minutes. A microwave, hair dryer, vacuum cleaner, these are fine for a few minutes at a time, but anything longer than 10 minutes and you are just killing the batteries.
Another option that will probably be way more trouble than it's worth is one of the 12-volt electric blankets (Road Pro) that pulls between 4-5 amps, which is a trolling motor type of amp draw, and you can cover the engine with the blanket and leave it plugged into the house bank all night. A single 12-volt Walmart battery could handle that, but two would be better for longer battery life.