Answer
Yes, if a compost reacts with water and receive the ($H^{+}$), the concentration of ($OH^-$) will increase.
Since the $[OH^-]$ increases, the substance will be considered a Arrhenius base.
Work Step by Step
Example: $NH_3$:
$NH_3(aq) + H_2O(l) --> NH_4^+(aq) + OH^-(aq)$
When $NH_3$ reacts with water, it receives one proton from water and increase the $[OH^-]$, so it is considered a Arrhenius base.
