"In this modern age it would be impossible for a state to wage war on another without any casus belli or cause of war. Even than that cause of war would have to be based on something morally righteous."

This paragraph is entirely incorrect. There's nothing "impossible" about invading another country without declaration of war, never mind a casus belli. As for the "morally righteous", please give me any example of a morally righteous war with the exclusion of the Second World War.

As for your question. We simply don't know. We have no existing records of any official declaration of war between Alexander the Great and Darius III. It's more than likely that some sort of communication happened before the initial Macedonian invasion, however, Darius didn't take Alexander seriously and simply ignored it.

Did Alexander have a casus belli? Sort of. Yes, every war had to be justified. If there's no justification, then good luck convincing people to fight and die for you.

The invasion of Persia was planned and prepared by Alexander's father, Phillip and the Greek city states. Their justification was vengeance for the initial Achaemenid invasion of Greece, Athens, and the enslavement of Greeks under Persian control. Similarly, the Persians invaded Greece under the premise that the Greek city states incited revolts in Greek majority regions under Achaemenid overlordship.

As for his invasion of India; possibly. The Achaemenid Empire's influence, at one point, stretched beyond the Indus Valley river. We know that Alexander contacted Indian rulers along the Indus river to pledge fealty. Some east of the river refused, and that was Alexander's justification. Other Indian rulers like Porus joined the Indus Valley armies in keeping Alexander out, which is why we inevitably invaded Punjab as well.

Alexander planned on invading the rest of India with no real justification. He also planned on marching on the Roman's in the west in the defence of Greek settlers in Italy.

So, yes, Alexander needed a casus belli fornhos invasions, although they were flimsy at best. Same went for the Persians before him and the Roman's after. There's not always a declaration, but when we're looking two thousand years back, sometimes we must can't find the record.