The background checking of C-family languages is a product of YCM's syntastic intergration (see :h youcompleteme-syntastic-integration
and :h g:ycm_register_as_syntastic_checker
). I don't see an easy way to set YCM to do that with other file types or to set syntastic to auto-update.
You might be able to dig around in YCM's code to see how they do it, then either extend that to work with MATLAB files or write a small plugin.