Can we use a fully custom HTML email template?

No, it's not currently possible to use fully custom email templates, but it's something that we're looking at. 

Here's our thinking on this.

The base email template that MageMail uses is a very simple, mobile-friendly, and effective email template. It's something that's continually being improved - for example recently we added support for smart image grids, where the size of the images in the grid adapts to the number of images being shown.

People are probably accustomed to creating custom email templates when sending newsletters and other types of email blasts. We believe that triggered email is fundamentally different from newsletters for a number of reasons.

The meat of a newsletter is the content - so you need to put time into content and a unique layout that will make the newsletter stand out and give your customers a reason to read the newsletter amongst all the other email that they receive.

The meat of a triggered email is really the trigger itself. And what we mean by that is that it's the time and the mechanics of the email that are the most important. If a customer abandons a cart an hour ago, the fact that they're receiving the email exactly an hour after that happened and that the subject line contains the name of the product and the contents of the email contain a photo of the product are the most important elements of it.

In addition to the functionality of being able to click through from an email and have the contents of your cart re-populated and even auto-logging-in the customer to smooth checkout friction.

Virtually all of our current customers go with the base template and it's very effective. So for these reasons, we tend to strongly recommend that people stick with it.

You could, in theory, put arbitrary HTML content into the body of the email - but it's not a primary use case that is well-supported and would be easy for you to do. For example, integrating template variables and dynamic content into that custom markup would likely be complicated. Also, the markup for the pre-header and footer aren't customizable though currently.