I am sure a Russian speaker would be able to use this method in Poland, Bulgaria etc.
I understand articles in Bulgarian Wikipedia, although I don't know Bulgarian, because there are very common words and it is obvious because the alphabet is the same.
Bulgarian grammar, however, is completely different: there is no declension, thereis a postpositive article and there are many tenses (Aorist, Imperfect, Perfect, Pluperfect) and moods. Verbs of both aspects have all the forms!
When I was In Montenegro, I used to speak some pidjin Serbian (grammar is closer to Russian: there is declension, no articles and many tenses are not used much in spoken language, but there are fewer common words and phonology is farther). Slavic languages are more similar to each other than Germanic and Romance.