You can change your locale after installing utau, however you cannot open utau with anything other than Japanese locale. You'd need to change it back to Japanese prior to using UTAU.
For what it's worth, nothing modern should be affected by your locale. Locale settings are mostly a hold over from older software made prior to Unicode (and it's proliferation) and prior to the idea that someone could possibly want to use a software internationally (imagine that). Coding for characters used to be separated by language and character code "coordinates" overlapped between languages, so they could literally only be one language at a time. (Eg, the coordinate A1 might be A in English, but A1 is also あ in Japanese, and ㄱ in Korean, etc). Because they have the same set of coordinates, the computer has to know which one to interpret it as, and the locale setting is what computers rely on for this. If the language the software was made in and the locale of the computer don't match up, the code is read wrong and it spits out whatever the equivalent is in the wrongly interpreted language's character set, resulting in gibberish (eg, what happens to utau when run under English locale. The underlying "coordinates" are the same, but you're seeing what they are in the English character set (many of the coordinates are invalid which gives you the question marks or blocks, and the other gibberish is the ones that coincidentally happen to be valid))
Hopefully that gives you a better idea of why it will always need Japanese locale to run properly. (Keep in mind I'm not well versed in coding and this is my not super technical understanding of how it works)
(Most modern programs aren't reliant on locale because they use Unicode, which includes multiple languages and gives every language its own unique set of coordinates in the code, so the computer can interpret all of them at once and doesn't have to choose)
TL;DR: You can change your locale after you've done the initial setup properly with Japanese locale, but you can only run UTAU with Japanese locale
[Edit]
The reason you need Japanese locale when you first download and install utau is because those messed up gibberish characters will get hard baked into the code if downloaded and installed under the wrong locale. It also causes other problems under the hood beyond just the displayed messages and characters being messed up.
It's been a while since I've had to change my locale for any reason, so I don't remember if opening utau under a different locale after it's been properly installed permanently mojibake's it, or if it only displays incorrectly and will return to normal once the locale is back to Japanese. My recommendation would be to just not risk it and not open it if it's not in Japanese locale, but if you just really want to know, you could always back up anything utau-related and experiment to find out if just opening it under a different locale causes permanent problems, and if it does, reinstall and restore from your backup