Example 1: you build Julia yourself from source with USE_GPL_LIBS=0. The Julia source code is under MIT, except the interface subdirectories noted in LICENSE.md which are excluded from the system image by USE_GPL_LIBS=0. No GPL code is linked or loaded in the system image. You can embed in a proprietary application and distribute* without any GPL obligation (MIT license applies).
Example 2: you link your application against the Julia download distribution, which loads GPL code and links to GPL libraries. If you distribute your application, then the GPL applies.
The libraries will never be compiled. The source shouldn’t even be downloaded.
That would probably be a good guess, but I don’t know (I don’t work for Julia Computing).
*Again, if this will impact your business: talk to an actual lawyer who knows something about open source!. There are also open source compliance companies, and Julia Computing mentions that an “indemnity contract” is available for Julia Pro (whether that covers open source compliance specifically, I don’t know – contact them directly).