The speedup only works on Mastabas and Pyramids. I'm pretty certain it doesn't work on Sun Temples, Mausoleums, and Obelisks. It will only work for the first monument you start. If you start a second monument before the first is finished, you'll get no more construction blessings.
Once the first Pyramid is about 70% complete, you won't get anymore construction blessings for it.
To take advantage of construction blessings, you should place the foundation of your largest Pyramid at the start of the game. This is almost always a good idea anyway, as it defines the spot for the monument, and you won't run into space issues in the future. Even with no one working on it, the occasional blessing from the god(s) may build up to 70% of that monument. You won't need any workers or construction materials for that 70%.
There are downsides, though. It will take a long time if you let the gods do it themselves. It also limits you to building only one monument at a time. Some players will have two or maybe all three monuments going at once to speed up the game finish. You'll also need to keep the gods very happy to get plenty of blessings, and that means lots of temples and/or shrines, and the occasional festival, which all cost money.
Personally, I look at the current scenario. Are raw materials for the monument abundant? If so, then you just need to get enough workers and industry going to gather them and build the monument, an occasional construction blessing being a treat.
Is time a factor and you have two or more monuments to complete? If so, you might not want to count on the gods to get them finished for you. Generally I start the larger monument first, especially if they are limestone pyramids. When the last few coarses are being laid, I'll start the smaller pyramid, allowing the workcamp workers to work on the foundation, while a few remainders finish the coarses and the stonemasons finish the outside of the larger pyramid.
The god that provided the construction blessing provides all the raw materials for you, so you don't need them. However, you will notice that if there were any sleds of bricks heading toward the monument when the construction blessing occurred, they'll be lost. A very small price to pay considering the amount of work and materials the god provides!
I have not noticed a difference in construction blessing "sizes." They all seem to perform the same amount of work. Some look more impressive than others, such as the additional coarses being laid versus foundation work. Also, if you receive a construction blessing while the foundation is being laid and the blessing completes the foundation, construction stops when it is finished. Even if all it did was fill in the last few grooves with rubble. Construction blessings that complete coarses, however, will always finish out their entire "worth" until you exceed about 70% complete. At that time, you will not get anymore construction blessings for the monument.
Personally, I like the Pyramid Speedup option. I don't count on it, but it is nice to have that additional help. Sometimes it can be frustrating, too. Importing materials for it, then a god finishes the monument for you, and you're left with a bunch of limestone you paid for that you can't sell.
Kuros Paladin - Knight of the Nile