Some 35-series (intel) jobs require a language and others don’t. Can I volunteer for language training and get sent to DLI?

You can volunteer for anything. If the Army has needs, you get lucky. I volunteered to be a millionaire....the Army did not have a need for that, so I did not get it. (When I get borded and forms are sitting around, I get dangerous. )

Check with personnel they should know for sure.

35N can go to DLI. I was a Plt SGT there at C Co from 2007-2009. But since the MOS is not language dependent dont look at getting restarted or rolled back if you start failing. Put in the 4187 and request the DLAB. If you score high enough request a class.