I can't remember whether it has always worked this way (overiding both DND and silent mode), but it isn't what is implied in the description under the Emergency Bypass switch. The description only mentions DND and not allowing sounds when in silent mode. The reason this matters came up while in a movie theatre the other night:
• DND schedule is set to automatically silence all alerts during the night (and automatically shuts off in the morning). This prevents my myriad of news, misc etc. alerts from sounding or vibrating all night.
• I have a number of clients that I want to still ring through and iMessages come through for even in the middle of the night.
• I was in the movie theatre, so before the movie began I was sure to flip the silent mode switch to "silent" and my Apple Watch mode to "silent" as well.
• During the movie, I got an iMessage from someone that I've set Emergency Bypass on for. My Apple Watch "dinged"! Thankfully my phone didn't go off in the movie.
• This means that before the movie begins, I'd have to go through each contact and shut off Emergency Bypass!
• Some may say "shut off your phone during a movie", but a better option would be: Apple Watch silently and discreetly taps my wrist or phone vibrates when an alert (especially a VIP client) messages me.