With all things being equal: shouldn't the GDP roughly increase equivalent to population growth (as a minimum, setting aside GDP increases resulting from technology, education, and all other factors).
Obviously there are a lot of factors that affect GDP. However, in general, GDP in one way measures the 'productivity' of a certain population. If that population increases, shouldn't it naturally follow that the overall productivity will increase proportionally (assuming normal population growth, rather than an influx of invalids, etc). I assume there would be time-delay in the response of the GDP, dependent probably on the nature of the population growth.