Applying it to every instance might not be trivial …
But it is :)
Per latest Unicode Reference, the following blocks are designated “Cyrillic”:
Cyrillic: U+0400 – U+04FF
Cyrillic Supplement: U+0500 – U+052F
Cyrillic Extended-A: U+2DE0–U+2DFF, 32 characters
Cyrillic Extended-B: U+A640–U+A69F, 96 characters
With this single GREP search you can locate any span of valid Cyrillic characters:
[x{0400}-x{04FF}x{0500}-x{052F}x{2DE0}-x{2DFF}x{A640}-x{A69F}]+
… it's a bit longish … I think in general it might be safe to simply use the 'standard' range 0400 – 052F, the “Extended” parts seem to be added for “Old Slavonic” and “Old Cyrillic” characters only.
Space and punctuation such as comma and periods do not fall in this range, so you might want to include them to grab entire sentences:
[x{0400}-x{052F}]([ [:punct:]x{0400}-x{052F}]+)*
will flesh out the entire Russian phrase inside
“How are you?” “???????, ??????. ? ? ????” “I'm fine, thank you!”
(It also picks up all of the punctuation right after that phrase, but theoretically that's not a problem. If it does, an even longer GREP could limit this to a “reasonable” set as well.)