Unless the person in question migrated to a country that doesn't use Cyrillic, everybody should be using Cyrillic to refer to that person, so in theory you shouldn't have to search with the Latin alphabet version of their name. Some letters don't translate easily, meaning multiple searches might be necessary. For instance, does the Cyrillic 'и' become 'i' 'y' or a combination of vowels?
"We aim to use the names that people themselves would have known and that would have been recognized in their own time and place.
This is true for the "official name fields", Proper First Name and Last Name at Birth, and it's also true for the "preferred name fields", Preferred First Name and Current Last Name. These are meant to be the names they would prefer, not the names we prefer to call them.
This applies for names with accented characters, and even for languages with non-Latin alphabets. WikiTree can accept most character sets, such as Cyrillic, Chinese, and Arabic."
I understand many people don't know Cyrillic and would have trouble with that. Many of us mono-lingual English speakers don't even know how to create those characters from our keyboard.
For instance, I see Ю́рий Гага́рин (Yuri Gagarin) is written in Latin script, but all of his family members are in Cyrillic script. So Wikitree has Gagarin-1 for Yuri, and Гагарин-1 for his father. Not exactly ideal.