Is it possible to stabilize wood with tung oil?

Basically, no. Tung oil neither penetrates far enough into the wood nor hardens enough to make a rigid block. 

However, it is still a lovely finish, even if it requires occasional maintenance. 

would it not penetrate enough if it was under a vacuum?  

It would, but it's still pretty rubbery when it polymerizes. 

Also it is likely to NEVER fully polymerize inside of the wood!  Basically you need a harder curing resin.