If I put 12 volts across a 1 ohm resistor, will it pull 144 watts?
Your calculations are correct assuming an ideal 12V source and an ideal resistor.

They will be reasonablly accurate using a power resistor of appropriate power rating and a reasonablly well regulated 12V source of appropriate current rating.

If you try it with a normal 1/4W or so resistor the thing will almost certainly go up in smoke. At that point it's anyones guess what will happen to the resistance, maybe it will go down as a result of carbonisation of the insulation, maybe it will go up as a result of burning away the conductor, you just don't known.