The short answer? No, absolutely not, The Greeks did not have the same concepts of sexuality as the modern world. They did practice pederasty (sexual relationship between a man and a boy), but for them it was a normal part of society that did not need to be explained in terms of "gay" and "Straight" (not that this means that everyone in ancient Greece partook in, or even agreed with, this practice). That being said it should be noted that only pederasty was accepted (in most cases anyway), and two grown men engaging in "homosexual" activities would typically be shunned by society. This is because once you came of age it was no longer "proper" to be on the receiving end of the relationship. So in that regard Alexander the Great most certainly was not "gay", though it is possible that he was in a relationship with an older man as a child and then vice versa when he came of age.
Now I assume, since your question is particularly vague, that your specifically asking about his relationship with Hephaestion, who possibly could have been Alexander's lover. If this actually was the case then it is possible that Alexander and Hephaestion weren't shunned, as others most certainly would have been, because Alexander was king and his men still had a great amount of faith in him. That being said, there is no direct evidence that Alexander and Hephaestion were ever anything more than two friends who cared a great deal for one another (which we do actually have evidence for). For example, Arrian talks about the morning following the Battle of Issus when Hephaestion and Alexander visited Darius' mother, and she mistakes Hephaestion for Alexander:
Darius' mother, in doubt...prostrated herself before Hephaestion because he was taller than his companion. Hephastion stepped back and one of the Queen's attendants rectified her mistake...the Queen withdrew in profound embarrassment, but Alexander merely remarked that her error was of no account for Hephaistion, too, was an Alexander" (Arrian, The Campaigns of Alexander 2.12.31)
Curtius and Diodorus both recorded the same story in their accounts of Alexander as well (though Plutarch quotes a letter supposedly written by Alexander that he never actually met the queen himself). Some confusion in regards to the nature of Alexander's relationship with Hephaistion undoubtedly comes from Arrian's account of their visit to Troy:
One account says that Hephastion laid a wreath on the tomb of Patroclus; another that Alexander laid one on the tomb of Achilles
The only problem with this however is that at no point in the Illiad did Homer ever make the claim that Achilles and Patroclus were anything more than friends. Patroclus was also older than Achilles and thus Achilles would have been the Eromenos, the young boy, in their relationship if it was a sexual one. Some Greek writers, such as Plato, did claim that Achilles and Patroclus' relationship was of a sexual nature, but it seems unlikely that this relationship would have continued after Achilles became an adult as well (given the contemporary view of two grown men being in such a relationship).
But it should also be noted that the Macedonian ruling dynasty had long asserted a claim of Dorian ancestry, and homosexual relationships between two adult males was much less frowned upon, and even accepted in some places, in Dorian Greek societies. So it is possible that Alexander and Hephastion had some kind of sexual relationship, even if there is basically no evidence that points to this being the case, because the Macedonians possibly might have accepted as part of Doric cultural practices. All that being said, however, Alexander still would not have been "gay" as we understand the word, because the ancient Greeks viewed things differently than the modern world does.