I definitely plan to look into the possibility. To do what you're asking, it would not be enough to define a new piece of UI in a script, but also to integrate it into the Tiled UI somehow, specifically the Properties view. Support for such things is not going to be automatic, but it's something that could be worked on. About the custom properties in general, there are plans to add support for data structures, arrays, enums and options like min/max value, in which case you may not need to code a custom UI. But all that is going to take time as well.
Viewing post in First Scriptable Development Snapshot comments
Without a proper design spec it's hard for me to argue this, but in my head I was thinking of a button which creates its own UI window and injects a string property into the currently selected object without needing to hook into the formal UI itself. Your version is definitely more intuitive, though. And support for data structures would indeed render my proposed script unnecessary (assuming it supports dictionaries which can contain arrays of dictionaries... I think that's as far down as I've gone so far, I guess, but a dictionary of [data type] and array of [data type] would handle it. The UI on that could get interesting, though).