That it didn't happen in OTl doesn't mean it can't. A different Russian calculation is possible especially as it was the minor German princes that suffered and not Austria from the treaty. Prussia took no territory from Austria but did annex Hanover. The deposing of a Divine Right monarch struck deep at the political foundations of Russia. So yes, a different Russian calculation is possible
What do you mean by "calculation"?
The only one that would make any major difference would be a decision to go to war (against the only European power whose interests didn't clash with theirs)and they are hardly going to do that just because they feel the King of Hanover has been hard done by.
And even if Russia did object, Prussia could easily satisfy her by agreeing not to annex all of Hanover - and taking some land from Austria and/or Saxony instead. That, iirc, is what King Wilhelm wanted to do anyway, and a Russian note would just have given him an additional argument to use with Bismarck.