No. It doesn't prove anything except that the person asking the question has no idea what morality is.
Morality, ultimately, is the ability to understand that selfish actions can bring harm to other people and to the society in which one lives, coupled with the ability to place more importance on the well-being of others than on one's own selfish desires.
It does not require the existence of, or teachings from, any god or gods to be able to understand that actions have consequences and repercussions.
Nor does the ability to curb one's selfishness require a divine origin. Some people may do so from a genuine desire to be a good person; others may do so simply from a fear of punishment (not necessarily the spiritual threats of their religion; perhaps under the secular laws, or even just from the disapprobation of their peers).
To claim that "if there is no God, there are no morals" is a rejection of the fact that people can be unselfish simply because they believe it to be the right thing to do, and means that the person saying so cannot even conceive of people capable of acting unselfishly without the threat of divine punishment or promise of divine reward - which suggests that he or she feels incapable of being moral without such threats or promises.