Most of the OP has already been answered, so much of my answer is pretty redundant. But I took too long composing it to just delete it, so:
It’s possible, if not probable, that Wilde would never have been prosecuted for gross indecency had he not sued the Marquess of Queensberry for libel. Had he not responded to Queensberry’s calling card (with its note addressing Wilde as “posing as a somdomite [sic]”), Wilde’s personal life wouldn’t have been subjected to such scrutiny. On public record, Wilde was a married man with two children; suspicions that he was gay–based on his mannerisms and what-not–couldn’t be substantiated without extensive investigation into his private life. And it was a lot of trouble (and expense) to dig up solid evidence of Wilde’s homosexuality, mainly in the form of statements from male prostitutes (admittedly, Wilde was naive to believe that these “rent boys” would never talk). Queensberry himself didn’t go to all that trouble until he found himself accused of libel, at which time his lawyers hired a number of private detectives to uncover evidence of Wilde’s sexual behavior.
In other words, Wilde could have behaved the way that he did (i.e., had sex with other men) and remained in England without being prosecuted, had he not been so reckless as to respond to Queensberry’s allegations and thereby put his own character on trial.
So I would slightly reword the central issue in your questions as follows: “if Wilde’s acts of homosexual conduct were made public knowledge (with evidence to substantiate the charges), is it likely he would have been prosecuted [elsewhere]?”
- In Ireland, the likelihood of prosecution would have been the same as in England. As a part of the United Kingdom, Ireland was subject to the same law under which Wilde was convicted, i.e., Section 11 of the Criminal Law Amendment Act of 1885, as can be seen in the Irish Statute Book.
2a. In the US, it would most likely depend on the state in which Wilde committed homosexual acts, and how that state defined “sodomy.” In the UK, “sodomy” was considered to refer specifically to anal sex, which was difficult to prove (without catching someone in the immediate act)–it was easier to get a conviction for “gross indecencies” which included ANY sexual behavior between two men (although as a misdemeanor, and not subject to as harsh penalties as sodomy). In many American states, “sodomy” had a broader definition, including oral as well as anal sex. It’s very likely (depending on the state) that based on the prosecution’s witnesses (the aforementioned rent boys, who testified to committing sodomy with Wilde) that Wilde would have been convicted of a more serious crime than the UK’s “gross indecencies.”
2b. In France, on the other hand, Wilde would have been in the clear, legally speaking. Sodomy laws had been struck down at the time of the French Revolution. If Wilde had fled to France, he would have been beyond the reach of the UK law, and would have been free to perform homosexual acts in France without fear of legal prosecution.
- As a woman, Wilde would not have been subject to the same charges or penalties, even in the UK. The “gross indecencies” law specifically applied to same-sex acts between men.
A famous story–possibly apocryphal–relates how Queen Victoria, when signing the 1885 Criminal Law Amendment Act (the “gross indecencies” law), was informed that the act didn’t cover “similar acts” by women. To which she responded, “Women don’t do such things!”
But, anyway–Oscar Wilde would have been better off had he been a woman or a Frenchman. Or had he not taken Queensberry to trial in the first place.