No, it wouldn't be correct. You can't play around with word order like that in English.
Unlike Russian and other more inflected languages, English doesn't have case endings. So it is impossible to tell, by looking at a noun or noun phrase, whether it is the subject or object of the sentence. The only way we can understand 'who does what' in the sentence is by the word order. We expect the subject of the sentence to come first. For example:
"My friend John communicated with you previously" = John communicated
"You communicated with my friend John previously" = You communicated
As for "Previously communicated with you my friend John", I'm sorry, but that sounds like nonsense. It's just a series of unconnected phrases that don't convey any meaning. Nobody would have any idea what you meant if you said that.