No. It's not possible to run a hook on checkout or update... so svn isn't going to be able to directly apply your patch.
I know you mentioned you don't want to convert your svn:external to an internal repo... However I'd most likely to go that route. The red book has a solid article on vendor branches. Hopefully the patch your coworker submits will be in the next release of the library, so you won't incur a cost updating to that new release and reapplying your patch - you could just go back to an svn:external at that point.
If that's not workable, other things that come to mind: having the build script apply the patch, or patch & build the library and publish it to an artifact repository (nexus or archiva) and having the team resolve the dependency from there.