Can a gear change snap my chain?
A chain is in danger of snapping when it develops a weakness. It will fail when the force on it exceeds the strength of the weakest park.

The rider might exceeds the strength of a weakened chain through high-force pedaling stokes, when accelerating from a standstill perhaps. 

Another way the strength might be exceeded is through a short but high 'shock' load on the chain, that might be induced by a gear change, but without very high pedaling force. Think of the 'clunks' you sometimes get when changing to a smaller sprocket in the rear.

What I suspect happened in your case is that the front derailleur imparted a lateral bending force on the chain at a weak point which in conjunction with pedaling force caused it to fail.