Would it?
Russia cant even stand up against Ukraine and is resorting to terror tactics in the false hope it'll break their will, when instead all its doing is pissing them off even more and galvanizing them against Russia and strengthening their will to fight.
With Ukraines stellar accomplishments against Russia so far, expansion of the war just involving NATO states on the border of Russia/Ukraine would probably spread Russia's military to the breaking point with having to deal with Latvia, Estonia, Lithuania and Poland.
Not to mention any other eastern european NATO members.. Though Slovakia, Romania and Bulgaria would probably mostly be used to keep Hungary and Turkey in check, since they are not exactly NATO friendly countries, Despite being in NATO, with their asshole leaders. Especially Hungary.
Which opens up US, France, Germany, UK and other naval and air powers to deal with China.. Not to mention any asian states that may choose to get involved out of fear of eventually being on the receiving end of China's expansion... Or currently facing the early stages of it Like Phillipines, Vietnam, Etc in the south china sea.
I cant see china doing the calculus on this and finding the conditions favorable.
Pointless.
You'd need 500 signed affidavits to be taken seriously. Anyone can just forge a signature. Affidavits are signed under oath, under penalty of law.