No it is not possible as the Warcraft III source code is not in the public domain (unfortunately).
You can attach assembly debuggers to the Warcraft III process at any time. However good luck finding a bug with one! If you are brave enough to try this my personal favorite is
ollydbg. Start WC3 and attach it to the Warcraft III process when you want to debug. Do note that doing this violates the Warcraft III terms of use, will probably get you banned from BattleNet if done while connected to BattleNet and is technically illegal in most countries.
However do not get your hopes up, I tried doing this for "compatibility between software" reasons (so that I could create a blp library that accurately reads blp files as their public documentation is terrible) and had practically no luck after hours of trying.