Is there any way to get Sublime text to update my pdf viewer (zathura) in real time as I write?
TL,FC (Too Long, For Comment)
Zathura will refresh the output whenever compilation takes place. Zathura has the option of enabling inverse search (using "synctex"). This is standard for the better Latex aware pdf viewers.
Thus it is down to the Latex editors compiler or previewer commands. Real Time is a "odd" phrase for repeatedly iterated compilation it is not a wysiwyg/wytiwyg/wytiwym live interpreter. That for personal users would be more like BaKoMa TeX or LyX but even LyX has to repeatedly compile TeX previews at intervals.
Several editors have a "preview" area where an equation or a paragraph can be compiled on the fly either as DVI, PNG or PDF etc snippet but it CAN NOT render the whole document with its cross-indexing fully (ToC LoF \Cite\index etc.)
Avoid attempting to have a script (timed or otherwise) it will almost certainly corrupt a partial compilation just at the wrong deadline. You need to compile your own Super-Duper-Syncro-tronic-Collaboration system with constant background incremental backups. (and we get many problems where they go wrong too).
It would be feasibly possible to build such an expensive "constant" Auto Compiling system (I think MS have dropped their experimental online TeX>MD editor) and it is generally those collaborative systems such as Papeeria / Overleaf who have the server resources needed. see http://docs.papeeria.com/compiler/auto/index.html