When I implemented the GNU APL mode for Emacs, I tried to make it as much as an IDE as possible. I modelled it on SLIME, and it has a live connection to your runtime, and provides things like jump-to-definition and completion based on the functions available in the runtime.

I even coerced SES (the Emacs spreadsheet) to act as an editor for large arrays.

I would argue that I have suceeded at least partially, such that I can say that it's definitely possible to implement an IDE for APL.