Since Mana Drain's trigger has to go onto the stack, whether or not both players have actively acknowledge it, it is assumed that it did and that both players passed priority thus allowing the trigger to resolve.
I'm not certain I would go quite that far, at least not without qualifying it slightly. Again, as I initially noted, the DCI policy is that untargeted mandatory triggered abilities that do not have a choice on announcement (such as mode) don't have to be announced. They are simply put on the stack. The resolution, on the other hand, is going to be based on shortcuts demonstrated during the game and/or how players are playing. And players do have to ensure their correct resolution.
Generally, yes, it will be assumed that the delayed trigger from Mana Drain is going to resolve automatically, as most people don't respond to it. But, given that you can respond to it (for example, with Abeyance or Orim's Chant), then there may be times where you have to specifically say you are responding to the triggered ability. Otherwise, you get into situations where intent has to be determined and the use of the shortcut previously has to be evaluated in light of the current situation.
So, it's not always going to be assumed that it did; just that based on how it has been played during the current game is how it is going to be assessed. Not to mention what was said when the last spell or ability was played (as that gives a pretty good indication of whether or not the trigger had resolved).