Certainly in relatively recent times (say, the past 60 million years) there have been deformations and distortions within the boundaries of what we now call the Eurasian Plate. For example, Joann Stock and I wrote a paper in 1994 called "Testing the Porcupine Plate Hypothesis," in which we argued that a certain section of the eastern Atlantic seafloor had NOT moved independently during the Eocene epoch; we were arguing against a hypothetical plate motion proposed by the Canadian geophysicist S.P. Srivastava. Our paper appeared in the journal Marine Geophysical Researches. Despite our skepticism on this particular point, it is certain that treating the northern part of the mid-Atlantic ridge as a perfect spreading center pushing apart the North American and Eurasian plates for the past 60 million years does not yield a good solution for all the magnetic lineations in the North Atlantic. An appropriate approach was provided by Swiss investigators Ziegler, Cloetingh, and Van Wees in the journal "Tectonophysics" in 1995. Their paper on intraplate distortions was part of a move away from the view that all changes in the configuration of earth's surface must be explained as the relative motion of perfectly rigid plates.
This relates to your question because the "sutures" at the former boundaries of Baltica can indeed still be identified, and it's perfectly possible that some intraplate stretching or squeezing could occur there. But there is nothing to propel the former Baltica into an independent rotation, is there? No spreading center within the northern part of the European continent, nor any major subduction zone to provide "slab pull."
As for the "what if" part of the question, some recent Y!A pundit answered one of those questions by asking "what if the moon were made of green cheese." Or maybe "what if France were in Australia." These questions are simply nonsense...that was his point.