Is there any way to place a medical alert symbol in a Watch complication?

That’s a star of life. Here’s another (and different) medical alert example.

There is no means to add additional watch faces to Apple Watch. What Apple ships with watchOS is what is available. And there is no star of life watch face available. (An app might offer a watch complication, but Apple has provided different and more direct means to access that info.)

If you are seeking to draw attention to the health ID info configured and available within Apple Watch or within iPhone, a notice posted on the main entrance door or on the refrigerator or wallet card can be an option, as can a watch band with whatever pattern you want, or the more typical medical alert bracelet or other jewelry with an inscription telling folks to check the watch or iPhone. (The primary care medical folks I have chatted with were surprised to have that data available in a device, so may or may not even look for it there.)

Log some feedback with Apple: https://www.apple.com/feedback/

For those unfamiliar with the medical ID: Set up your Medical ID in the Health app on your iPhone - Apple Support

I’m not sure what you’re referring to as “a compilation”, particularly in the context of an Apple Watch as shown in your footer here.

Could you explain a little more about the app or document or field where you’re trying to add a “medical alert” symbol?

Also what you mean by a medical alert” symbol, as I’m not aware of any standard used there. Most use some variation of either a red cross, or of a star of life, or a caduceus.