You won't burn the house down, but you'll ruin one or both chargers.

The Hobbico 12V charger you're talking about is a simple transformer, and its voltage actually varies anywhere from 18V to 10V depending on the load placed on it. In addition, it's only capable of producing a few hundred milliamps of current.

What you want is a regulated power supply that can produce a steady voltage between 12V and 13.8V, and produce enough Amps to supply the demands of your charger (at least 5 Amps, probably closer to 10 Amps). Hobbico sells a regulated supply, as does Radio Shack. On Ebay, you can pick up a pyramid supply for a reasonable price.

You can connect your Hobbico charger to a 12V battery to supplement the battery. The battery will act as a regulator and keep the voltage in a range that's compatible with the charger.