Is it possible to create a FCP effect inside Motion that puts an opaque box behind a title?

This is an interesting idea.

Unfortunately, I don't see how it could work.

The problem is that the Motion template does not have any way to access the text parameters of a title in FCP; it does not even "know" if it applied to a title or a video clip.

What can and does work is creating a title in Motion (not an effect), and have that title include a box behind the text. Your idea of using align and link behaviors is solid, and is how this is usually achieved.

Here is an old but still very relevant video where Mark Spencer of rippletraining explains how to make such a title:

https://www.youtube.com/watch?v=Blb1WHrbJdk

You could just build the template you want AS an Effect, not a Title. The background box can be placed and sized behind any text you use in the Effect. The Effect can also be added to any other Title, you just won't be able to automatically place and size the boxes behind the texts of the other Titles.... but you could just delete the original (other) Title texts to be replaced by your Effect.

You WILL need to publish the Text attributes you want to be able to customize as well as the actual Text (textbox) so that you can edit the text — you will not be able to edit the effect's text in the Viewer — only in the effects inspector.

The effect you build can be used on any media, other Titles and Generators as well. Losing the ability to edit the text in the viewer is a small price to pay for the flexibility.