I used to play the 3...Ng4 line, probably played around thirty serious games with it in all, and the problem I had was that in too many games White managed to swap off a few pieces leaving him with a small, but undeniable, advantage.
If you want to live dangerously learn the Englund Gambit - 1.d4 e5! It's terrible, but there's just one spectacularly winning line for Black which may occur once every ten games and makes the nine previous losses worthwhile!
Originally posted by XanthosNZDefining what is "sound" by appealling to "current theory" is a circular argument. Openings don't generally win or lose games in and of themselves below the GM level (if there). If an opening gets you a playable game in the main variations, I'd say it's sound. Since the Budapest does so, even if there may be a slight advantage to White in theory, I'd say it is sound.
Whether according to current theory and best play the opening will give good results.