It shouldn't really matter either way, but the answer is no.
First, Sulu is a character written in the 1960s and on TV the official story was that all heroes are hetero. Trek is a show of its time and the characters are rendered in terms of norms of that period. Trek was pushing the envelope by simply being multicultural.
Second, alternate reality Sulu puts the moves on Uhura. This is not knock-down proof, since this is not regular Sulu, but as evidence it stands for rather than against the hypothesis that Sulu is straight.
Third, we get no direct on-screen evidence suggesting that Sulu is gay. Not only is it not mentioned, it's not even hinted at.
Fourth, Sulu's daughter. Sure, gays can adopt kids, and gays sometimes involve surrogates to have biological offspring. Again, this is not knock-down evidence, but the most typical father-daughter relationship is that of a biological pairing (which would mean that Sulu would, at least, appear to be bisexual). Conventional expectations are still such that we that when we speak of father and daughter the presumption is that the relationship is that of a heterosexual father and implied mother who produce the daughter. Cutting against the grain of this default expectation requires introducing more data. My default expectation of the faucet, for example, is that water will stream out if I turn it on - to defeat this default assumption, we need extra data (e.g., the plumbing is broken).
The standing presumption is has been Sulu is straight for quite some time. For example, people back in 1976 discussing the show did not worry themselves about whether Sulu was straight or not.
Since presumption is in favor of the belief that Sulu is straight, the burden of proof really lies with the person who suggests that he is gay. The case above is not an absolute slam-dunk, but neither is the case against Uhura smoking pot in her private quarters. Want to assert that Uhura was toking in her private quarter? Fine, you have the burden of proof.