Ye, Script Studio fully supports Unicode input and Cyrillic and its assoiated diacritics that when combined make up a single character.
Input of these special Unicode characters varies depending on your operating system and keyboard set-up but you can usually do this with keyboard shortcut combinations of the Option/Alt key and regular keys.
You can also select Insert Symbol from the Edit menu to choose from a character map of unicode characters.
The software also supports right-to-left input and presentation by selecting Text Direction > Right To Left from the Format menu.
Depending on the language you are writing in, you may need to install a specific font that supports all the glyphs in your language's character set in order for your text to display, print and export to PDF correctly.