Of course you can, it's emacs!
(info "(org) The export dispatcher")
‘C-a’ Toggle asynchronous export. Asynchronous export uses an external Emacs process that is configured with a specified initialization file.
While exporting asynchronously, the output is not displayed. It is stored in a list called “the export stack”, and can be viewed from there. The stack can be reached by calling the dispatcher with a double ‘C-u’ prefix argument, or with ‘&’ key from the dispatcher. To make this behavior the default, customize the variable ‘org-export-in-background’.
So, you can export asynchronously to PDF like this: C-eC-alp.