Dear Nampuna, yes it is possible! LaTeX is a syntax-based compiler, which means you can push your tables in a LaTeX doc and compile them from within Stata. This requires a good knowledge of LaTeX syntax, and paths where the TeX compilers are installed. A lot of guides exist on this topic.

A quick work around is to install texdoc http://repec.sowi.unibe.ch/stata/texdoc/ which has most of the stuff built in.

On table numbering: LaTeX automatically assign table numbers. Caption is just to add some text to the header and the label is only needed if you are calling the table from the TeX doc. Since you are mass producing tables, I am assuming in a sequence you want them published, I would suggest you drop these two. Unless you want some customization which can be done within the loop in Stata.

This is an interesting question and I might do a guide on this since it also deals with Stata's ability to run other programs from its command line.