May be possible when you write a plugin for Acrobat.
If you want to completely automate it (without any manual steps) then this means that you will be using Acrobat as a server and AFAIK Acrobat license does not allow you to do that. You need a server-based solution, like LiveCycle to do that.
You can use Actions mechanism in Acrobat XI Pro to do that but you'll need to perform some manual steps to launch an encryption action that you create.
You cannot write an Acrobat plugin that does that because Acrobat SDK does not have functionality to encrypt PDF in a plugin. You can use Acrobat SDK to write a stand-alone application that does that but this quite a bit of work.