No, you really don't want to boil the entire mash--that would denature all the enzymes! You'd end up with a very starchy beer.
With a traditional decoction mash, you typically wait 15 minutes, then pull 1/3 of the mash (a thick pull: mainly grain plus a little wort) to be boiled. The reason behind this: what's pulled contains relatively little enzymes, the assumption being that they have been dissolved from the grain into the liquid. As such, boiling the grains does little to reduce the total diastatic power of the mash.
If you boil the whole mash, you'll destroy all the enzymes, leaving you with only a partial conversion--a lot of starch and little fermentable sugars.
Once you've boiled the whole mash, there's no point trying to cool this to do any rests--all the enzymes that perform beta glucan, protein, and saccharification rests are long gone. Furthermore, the rests in a decoction are the same as any other method of raising the temperature in a mash (infusion/direct heat). However, historically decoction was effective in the absence of accurate thermometers, since it allowed the brewer to hit rest temperatures by measuring the volume of the decoction rather than by directly measuring overall temperature.
If you wanted to experiment--and I stress experiment!--then you could boil the mash after the normal mash is complete. This may increase the quantity of melanoidins. If you try that, please post your results!