I never tried doing this and it's not something officially supported. Under the covers, Tinkerer just calls sphinx-build with html output, you could try a sphinx-build with latex output then use pdflatex as per Sphinx documentation:
http://www.sphinx-doc.org/en/stable/invocation.html That being said, Tinkerer hooks up a number of extensions to the html builder events, so I'm not sure how much of the stuff Tinkerer adds on top would still work for another builder (also not sure how much of it you really need :)). You should give it a try and build your blog using latex builder and see if things look good enough for you needs.