No.
If you assume that R'hllor is a 'real' god, and his priests and priestesses are correct about their religion, then you also have to assume that his antithesis, the unnamed god of ice and death, must also exist.
That makes at least two "real" gods if R'hllor's followers are correct.
If you base the assumption on the tangible results obtained by those who pray for R'hllor's favor, then it seems likely the Old Gods are, or at least were, at least as real as R'hllor and his antithesis.
The Children of the Forest, and a few others (such as Bran Stark), receive equally tangible results from the "old magic": seeing through the eyes of the faces on weirwoods; possessing the senses, or even minds and bodies, of animals and weaker-willed humans; or even prophesies that are at least as accurate (perhaps more so) than those of the followers of R'hllor ("greenseers" such as Bran and Jojen Reed have "green dreams" that reveal the future).
The followers of the Many-Faced God also have tangible results from their worship, not the least of which is the ability to take on another's actual face through magic.