Can the notation for polynomial reduction, A ≤p B be reversed in computability theory?
The notation $A \le_pB$ means problem $A$ can be reduced to problem $B$ in polynomial time, and that $B$ is at least as hard as $A$, because solving $B$ means solving $A$.

$A \le_pB$ $\equiv$ $B \ge_pA$

It does $\mathbf{not}$, however, mean $B \le_pA$, and to claim as much you would have to show the appropriate reduction.