Deleted Post. Needs more work.
Bern
Thanks for sharing and the well-worded caution. 
One question, does Mail Act-on also move Mail attachments with the email to DTPO? Cheers.
Hi Allsop
I think it will HOWEVER, I’ve been playing with this a bit and have managed to break it so it continues to move email to Apple Mail archive and does NOT import to DTPO. Until I get my taxes done I’m not going to sort it out. If I could delete this post I would and repost later.
There are three Mail Rule apple scripts available- Add attachments to DT, Add messages to DT and File messages & attachments. I haven’t played around with them enough to say what the other two do alone or in combination.
Sorry for the premature post. 
Yes, I have downloaded the app as a trial and it is doing exactly that—not transferring stuff to DTPO, now need to disable it!
Well it’s weird as the outbox rules seem to be working as it imported an email I just sent and the inbox rules were working. I’m going to need some time to see what’s behind this behavior.
Sorry for wasting your time. 
4/11/16
Post deleted. I need to look further into this before re-offering it.
Bern
It’s been a while since I’ve used Mail Act-On, but it is not needed to run script rules on incoming mail. Mail Act-On does allow you to set up rules for outgoing mail, which is something Mail.app doesn’t do on its own.
For what it is worth, I used MailTags and Mail Act-On for several years and while both apps provided some nice enhancements to Mail.app, I found them to also be high maintenance apps that often broke in one way or another with every update to OS X.
Worse still is the fact that you cannot process email on iOS and still expect all rules to consistently work on the Mac due to the fact that the rule triggers may change (mail is no longer unread, mail moved, mail responded to, etc.). That’s true of mailbox rules even if one doesn’t use MT/MAO.
Thanks Greg I hadn’t given a thought to IOS mail implications.
What attracted me to this was handling ALL mail (in and out) allowing me to look for and focus exclusively in one place. If only incoming or outgoing mail gets handled and I need to deal with Apple Mail regularly for the other half the idea loses its appeal.
That MAO lacks robustness around these moving scripts will likely postpone my dealing with it for now.
Thanks again for sharing your experience.