What is the Big O of T(n)?
Yes, all functions $f(n)$ satisfy $f(n) \in O(f(n))$. The definitions are meaningful even if $f(n)$ isn't the running time of any function. Indeed, this notation comes from number theory, where $f(n)$ is usually some error term. Even in computer science, sometimes big O notations is used while analyzing algorithms for something other than a running time or space requirements.