Does it make sense to examine properties of $(G,\circ)$ if we, in the meantime prove that $(G,\circ)$ is not a groupoid?

Question

If, for example, we are given a set $G$ and an operation $\circ$ and we have to examine properties of that operation on that set (closeness, associativity, commutativity, exsistance of neutral, exsistance of inverse), should we continue with examination if we find out that the given set is not closed for that operation?
That would mean that the ordered pair $(G,\circ)$ is not groupoid. Does it make sense to examine other properties if $(G,\circ)$ is not groupoid?