Yes, in the US and most of continental Europe, multiple charges are usually first summed, then sentence determination is done by court order and then penal enforcement rules kick in after the verdict (2 years sentenced does not always mean 2 years served). A 1000 years' sentence has a greater non-parole duration than a life with parole; it is likely that he will serve life with no parole.
IANAL, though.
At least in France, this article says that for similar concurrent charges (not sure how similarity is determined), the most important sentence is picked. So, max instead of sum.