I dont think speed chess of any variety helps with your tactics per se. It encourages curtailed thought processes, and most folks dont go over most of their games afterwards. There might be some reinforcement of tactical motifs you already know, but there could also be some bad habits picked up in terms of thought processes. Anyway, this is only question one.
Question two is, even if speed chess can help your tactics, can bug house/crazy house do so? Its a given that many of the tactical situations are quite different from those that arise in an actual game, but it doesnt seem terribly likely to me that this will mess-up your analysis of traditional positions -- more so just that the % of tactical situations that you can learn from is lower. Of course, the games are played in a more bloody and tactical manner so there are more tactics overall. Thus, I see the major difference being that most people dont ever go over bug/crazyhouse games and learn from them (especially bughouse games).
So my conclusion is that, if you can learn tactics from speed chess at all, something I'm skeptical of, then you can probably learn tactics to roughly the same degree from crazyhouse/bughouse, provided you go over the games to the same degree (which almost no one does, especially with bughouse).
I have heard people argue both ways for this question and wanted to hear people's opinions