Well, if it's not working exactly as you'd expect (select text from PDF, paste into InDesign, see Cyrillic text in ID) then there are about 80 different ways that it can go wrong. The most critical issue is that you'd need to select a font in ID that supports Cyrillic before pasting. The next most critical issue is that we have no idea how that PDF is encoded - there may be no way to get meaningful text from it without vast amounts of work.
Have you tried it yet? What happened?