Does this mean I could post some untransliterated text here in a comment and make your browsers all do these computations?
Unless you install special rules you won't be doing extra computation.
Lynx does[1], but it does that using iconv, which I think doesn't use UTS #35 transliteration rules.
[1] https://lynx.invisible-island.net/lynx2.9.3/CHANGES.html#:~:...