Use expression for a property value in custom visual?

For table and matrix mappings, it will work if you just want to populate a single property, which is how I've interpreted your original question - essentially like the way the Title text property works in the standard Title menu.

Although yes, it likely won't work if you want to do data bound mapping (e.g. rows to colors).

I've implemented this approach in the HTML Content visual, which uses a table mapping. It works perfectly fine for the "No Data" Message property:

Here's a link to the location in the code where it's implemented so that you can hopefully take this and use it, if it suits your use case.

There's also a second property in the source code beneath the linked one, and this should turn up in all reports shortly, once the visual has been fully approved through to AppSource, but both work fine.