@muzicman0 

Yes, it should be OK, look at this.

  @muzicman0 

I assume the reason for this unusual mount position is aesthetics? 

I think you should find a better spot than on top of a pergola beam and here are a few reasons off the top of my head:

-what colour is the pergola beam and what is it's surface temperature after a full day baking in the SoCal sun?

-case is designed for vertical mount and the 225-outdoor case is far less weatherproof than the 610/650 are

-how are you going to protect the cable and anything it connects to from lightning?

-curious wildlife possibly finding it a fun toy or novel snack

-eventual UV breakdown or heat deformation of plastics allowing water ingress at antenna ports or in the etherjack area

I would really advise against your plan.  I have had great success spraying my 225-outdoors with Krylon paint for camoflage if that helps, but mostly I'd suggest you mount the AP on a nearby building wall, or on a support post for the pergola itself.

  @muzicman0 

Glad the info was helpful.  Based on your additional detail I have a few other thoughts:

The AP could be mounted behind a flat piece of colour matched polycarbonate plastic (probably white) which could be made flush with the stucco surface on the underside of the beam.

You could also leverage the fact that the EAP225-outdoor antenna ports are standard SMA-antenna jacks and leverage aftermarket flat anteannas, again keeping with the idea that you want the antennas to blend in with the structure and ideally colour match (be paintable).  You don't have to use the included 4" dipoles and I'm sure TPlink would be willing to share which port (left or right) is the Main and which is the Diversity if you only used a single patch antenna per AP.  The antennas being flat and passive could literally be blended flush with the stucco with a skim coat.

I would imagine you are also installing speaker systems, and could leverage those wire paths for your ethernet cables and the speaker mounting area could also support a discrete external antenna, maybe with the AP itself mounted to the back of the speaker.

Best of luck on the install!  Love to see some pics of your final solution.