Nah. They'd probably be better off striking the UK than the US for a lot of reasons if they did feel the need to strike directly at a NATO member and risk article 5 being triggered. That said, the war is still asymmetric enough that the grinding war of attrition does seem to be a channel the Kremlin would be wise to stay in, with any directed retaliation for the long range missiles carefully calculated.

Strangling the energy supply to the EU during the winter may well be a solid enough method -- their likelihood of dodging a bullet on weather with a mild winter two years in a row is pretty low -- buy the strategy right now seems to be to pry the EU away from America, rather than galvanize the alliance.

Truth be told if I were Putin I'd likely be looking for a very symbolic response that won't force Trump's hand to escalate.  Giving Ukraine long range missiles and the authorization to use them to strike Russia was Biden's way of flipping the checkerboard, and poisoning the well that Trump just won from him. Putin does have to save face, but he doesn't have to walk right into Biden's trap. 

 hitting a factory that makes these Storm Shadow cruise missiles in UK would probably make sense 

of course the UK media would say it was not a weapons factory but some kindergarten that was hit by Putin and show pictures of dead children from Gaza as proof