That is correct, but if GDP remains stagnant or falls, that becomes harder to do. GDP per capita is one of the ways that the wealth of a nation's citizenry is measured, so if that is declining due to low productivity and continued population growth, that's trouble. Basically means that the economy isn't going to be able to serve people.
I understand what you're saying, but I don't think looking at GDP to the exclusion of other factors is a very useful exercise.
If GDP per capita is the way you're measuring wealth, you're not doing yourself any favor by adding more people to the denominator. Also, having a higher GDP doesn't help if it means everyone is burdened by the additional strain of providing for all the people who are out of work as a result of whatever policy you used to goose GDP.
Right. It's basically an unresolved empirical question as to whether or not bringing all of those new people here will result in the release of a magical growth fairy that will paper over any of the problems. If it does, glossing over the whole question isn't too bad. If it doesn't, then you're right.
