Sure you can. You can greatly increase your immigration by increasing gdp/c,social services,etc..
By reducing the other regions abilities to keep their population happy.
Ive got a game playing now where my net anual migration is over 1 million a year.
Ive seen games where it was a net migration of over 4 million a year.
By the ways, your idea about adding in paying people to move to your region is a very good idea i think.
Ireland does it now in real life. It would make an interesting addition to the game i think.
Id throw it up in the wish list, but its your idea,so ill wait and see if you do first.
The apocalypse is near if we agree on something.
While some of your population increases through migration are impressive it still would take quite a bit of time to empty your enemy's population, probably longer than a scenario lasts. Still it is an interesting ploy to weaken countries with a larger population. You'd really have to have a hot economy to absorb a huge host and maintain your GDP/c. Or you're imminently going to war and need cannon fodder.
I'll go ahead and post a wishlist item for bribing people to immigrate into your region via negative immigration fees. That would make an interesting choice for players regarding immigration. If BG can make negative immigration fees then maybe they could also do emigration fees both positive and negative so players could even pay their citizens to leave for other regions to reduce populations in order to improve GDP/c or to pay them to stay if some other region is enticing immigrants.