Disclaimer: The following screenshots were obtained through a HEAVILY MODDED game, in which I decided to test the limits of immigration by directing all immigrants in the world to Haiti. The results is as you see below. The purpose of the experiment was solely to determine the volume of immigration in an entire game and not to become a tremendous world power. Nevertheless, Haiti at the end of the game was an impressive beast.
Secondary Power? Secondary to one country, I guess. Of course, since I only had one province I couldn't become a Great Power, but that wasn't the point.
Immigrants were attracted to Haiti by a +10,000% modifier to both provincial and global immigration in Haiti's jurisdiction. I also increased RGO size tremendously (each of Haiti's four provinces could accommodate 12,000,000 in its RGO), and the liferating of the provinces were given a modifier boost. Oddly, this did not translate into extra population growth.
Craftsmen will only immigrate if there's work, so I had to build factories. To accommodate my population of 160 million, I had to modify the saved game several times. I gave Haiti a level 99 cement factory to begin with. I soon had to edit it to become eight Level 99 factories. Then level 199. Then 299. By the end of the game, I was dangerously close to filling eight level 400 factories, with almost half my population as craftsmen and almost half as artisans.
There are a few very odd things here I haven't shown. For example, Mahayana and Shinto were pretty big minority religions.
The conclusion of the experiment? The massive diversion of immigrants significantly weakened the Americas, but the usual suspects ended up in the sweet sixteen. The net volume of immigrants translates to roughly 160 million people (given compounded growth of those immigrant communities). It can make you incredibly powerful, but on its own it can't make you number one. Britain and China were the only two countries more populous than Haiti. Great Britain had industrialized India and edged me out, and all the world of immigration couldn't change that.
And that's the strangest screenshot I've ever made, cheat or no.