2.36 (1966)

Yes, it is. By (G. Nöbeling, Invent. Math., 6 (1968) 41–55) the additive group of all bounded integer-valued functions on an arbitrary set is free. Hence the group of all continuous integer-valued functions on the Čech compactification of an arbitrary discrete space is also free. For any compact space $X$ there exists a continuous mapping of the Čech compactification $Y$ of a discrete space onto $X$. This induces an embedding of the group of continuous integer-valued functions on $X$ into the free group of continuous integer-valued functions on $Y$. (V. I. Kuz’minov, 1969.)