No, it cannot be said.
Certainly not about English, because it would mean that a majority of English speaking population would usually talk mostly using words from a closely related language - that would be what, Frisian? - with English accent and grammar.
That might maybe happen in Scotland, where English and Scots might intermix in this way, but this kind of speaking is far from majority.
It certainly is not the way here in Germany, people won't, for example, speak Dutch using German grammar and accent. They either speak Niederdeutsch or standard German. They might speak more or less in a dialect, but a dialect is not a language, Ukrainian is certainly not just a Russian dialect, they are several grammatical differences like the vocative case which Russian lost half a century ago.
It doesn't work for Russian at all, Russians don't usually mix their language with other closely related languages. Only when they try to learn that closely related language as a foreign language this might happen.
It can come out this way in former Yugoslavia, because the language there is mostly a dialect continuum and the languages are really only separated for political reasons - with the exception of Slovenian (which lies between South and West Slavic languages, that is between, say, Slovak, and Croatian) and Macedonian (which is closer to Bulgarian).
Slavic languages are a hobby of mine so I do know a lot about them and can speak several.