Levels that do not have any custom textures or scripting will work on average about 90%, considering replaced object types with new behaviours and linedef types with nicer setups. Lua scripts that modify the player (state/flags/etc) are quite likely to break, but those that don't are quite unlikely. All graphics will need to have their palette updated using SLADE, custom textures and flats are otherwise fine but sprite names and groupings may have changed. The one thing that definitely needs to be reworked is characters. Vague details of the system are out there already but I intend to release a testwad explaining what is necessary whenever release ends up happening.
No program to convert anything other than the palette for graphics exists, and is unlikely to.
(source: am an ex-dev with benefits)