While the legalities of the Open Gaming License prevent me from making statements of compatibility, I can say from personal experience that I have run games where characters who were generated under the 1st Edition AD&D rules were able to function in an Adventures Dark and Deep game without any problems whatsoever. You may draw whatever conclusions regarding compatibility that you wish from that.
Adventures Dark and Deep is not, however, a clone of the 1E rules. It is an attempt to present a "what if?" scenario. What if Gary Gygax had been able to continue developing Advanced Dungeons and Dragons? It uses the 1E rules as a starting point, but includes new classes (as described by Gygax in Dragon magazine), a streamlined combat system (based on third-party accounts of how Gygax ran his own game at tournaments, as well as other sources), monsters being given variable hit dice (so a giant might use a d12 for hit dice, while a kobold would use a d4), tons of new spells, magic items, and little changes throughout.
So, it's not a copy of 1E.
It's not just 1E with some new stuff bolted on.
It does use 1E as the launching pad for various additions, changes, and refinements, but doesn't take things way out into left field.
And, to clarify, it's not just 1E with my own house rules. It's the result of many, many hours of research into Gygax's public statements as to what his version of a second edition would have looked like. Whenever I feel myself getting too self-indulgent, I repeat that design goal like a mantra, and everything comes back into focus.
My advice, download the three books (they're free, and you can find the link over at http://www.adventuresdarkanddeep.com
), and check it out.
Hope that helps!