Weak Decisional Diffie-Hellman Problem
Yes it is. It can be formally reduced to the hardness of the decisional square Diffie-Hellman assumption, which states that distinguishing $(g,g^a,g^{a^2})$ from random is hard (this is a well established assumption).
It follows in a relatively simple way from the answer I wrote here to a related question. I can let you work out the details in case you want to play a bit with these reductions. In case you cannot figure out the formal reduction, just ask in the comment and I will elaborate.