Hi, economist here. There's lots of very robust theory already on what you'd expect to happen if a bunch of people unexpectedly came into a country. If you're looking for me to describe it in terms like "good" or "bad," then economics isn't for you. Whether it's "good" or "bad" really depends on where your priorities lie.
First of all, a one-time increase in the population size will increase GDP of a country, but decrease that country's GDP per capita. So in a sense, all those articles you cite that say GDP growth is rising in countries taking in refugees, well, that's to be expected. But it's also to be expected that GDP per capita will enter a lower growth path. This is a very straightforward implication from your typical exogenous growth model.
To understand the intuition behind this, imagine the economy's output (Y) like this: it's technology (A) times capital (K) times labor (L), or in other words, Y = AKL. This sort of makes sense, right? For example, if you double the number of tractors and double the number of farmers, you should be able to produce double the amount of wheat. If you upgrade your tractors, then A increases a little, too, and everyone gets more productive.
But now consider the following: if there are lots of tractors and not many farmers, adding in extra tractors doesn't increase productivity much. If there are too many farmers and not a lot of tractors, adding more farmers doesn't increase productivity much. So our original equation was wrong; we need a way to account for "diminishing marginal rate of substitution." This equation works fine: Y = AK0.5L0.5. In this equation (called the Cobb-Douglas production function) doubling both labor and capital at the same time also doubles output, however doubling only labor and keeping K constant does not double output. Therefore, GDP per capita (Y/L) falls.
So what we see when a bunch of people enter into the economy all at once is that L increases, and K stays the same. Obviously output (Y) increases, but it increases less than one-for-one with Y. Therefore, Y increases, but Y/L falls.
Second of all, the above story is useful but admittedly it's a bit oversimplified. The truth is that many Syrian refugees are actually pretty well educated! So we need to add a fourth variable to the right hand side of our equation: human capital, which is econ-speak for how smart people are. The effects of human capital are a bit ambiguous here, but it's safe to say that if Syrians are well-educated on average, then that might increase GDP even more than what the simpler model above suggests. And no, it's not necessary that the average Syrian has as much human capital as the average German for that effect to happen. These effects, however, would take place more in the long-run than the short-run. So overall it's hard to say whether or not GDP per capita would actually fall. Empirical evidence on this is mixed.
Third of all, overall GDP of the world economy will unambiguously increase; as a corollary, world GDP per capita will increase. The intuition behind this is simple, going back to the equation Y=AKL: people are moving to countries where they can be more productive, so world GDP increases. At the same time, the world's L stays the same; people are just moving to places where there is a higher A and higher K, so marginal productivity of each unit of labor increases.
This is the main reason why so many economists support open borders: the effects on a country's GDP per capita are ambiguous in an empirical setting, but the effects on world GDP per capita are very positive and very unambiguous. So if you mainly only about your fellow countrymen and you don't really care about the rest of the world, then taking in refugees is economically risky-- it may increase the welfare of your neighbors in the long-run, or it may not (also, consider that maybe one day you'll consider those refugees your neighbors? Hm?). If you place equal priority on all people around the globe-- if you think the welfare of a Syrian person is just as important as the welfare of a German person-- then more or less completely open borders should be your policy of choice.