I’ve not seen any code that specifically catches the deferral, however, if you can capture either Exit Code:
- 1618 - Exit code used when a UI prompt times out or the user opts to defer.
- 60012 - Exit code used when a user opts to defer.
(Source: AppDeployToolkit\AppDeployToolkitConfig.xml)
This would handled in the Show-InstallationWelcome function (from ~ line 8640 in AppDeployToolkit\AppDeployToolkitMain.ps1)
I vaguely remember there was an extension that another poster had written to give the user more control over the deferal, i.e. gave the user a date & time when they would like the installation deferred to. It looked quite a good addition to the Toolkit.
However, I can’t remember exactly, But I think it had some functional issues, and I think the OP of this other thread went quiet, so the issues never got fixed. I also believe I saw recently that someone was hoping this feature / change to the deferral process might get included in v4.0 of the toolkit 
.
FYI: v3.9.3 is currently the latest version of the Toolkit - There are quite a few bug fixes since v3.8.4, so it might be worth giving that a try and see if this gives you some further options
Release Notes: