So, instead of going through the motions of changing my keyboard, I have been just using the English letters sometimes, instead of using the Ukrainian letters all the time. Does that still make it Ukrainian?
Unicode makes a distinction between Cyrillic letters and Latin letters, even when they look alike. For example, Latin 'i' is assigned code point U+0069, while Cyrillic 'і' is U+0456; Latin 'a' is U+0061, while Cyrillic 'а' is U+0430. Unless DuoLingo is programmed to translate Latin characters into their Cyrillic visual counterparts, typing Latin letters instead of Cyrillic ones won't work.
Duolingo does make some automatic transliteration but there is no guarantee that it will work fine for a particular Cyrillic sentence you are typing.
That's essentially the system that lets you omit accents and type ae instead of ä.