No, the dimensionally correct equation may not be a correct physical relation. Consider the following relation, v = u + 2at
The dimensional formula of v is [LT-1] and that of (u + 2 at) is also [LT-1]. Hence, the above equation is dimensionally correct. But, it is established fact that the above equation isn't correct physical relation.
O the other hand, a dimensionally wrong equation can't be a correct physical relation. For example, v = u + at2 is a dimensionally wrong equation and it is also a physically incorrect relation.