Not at all. The internal speaker of a Mac will play any "system notification" sound effects.
Here's[1] the macOS audio mixer. I've right-clicked a source here. Notice the separate "Sound Output" and "Alerts and Sound Effects" choices here. By default, external speakers will be used for "Sound Output", but "Alerts and Sound Effects" will stay pinned to the internal speaker.
[1] https://i.imgur.com/2Z0GB04.png
The simplest way to notice this is to empty the Trash on a Mac Mini (or a Mac Pro.) The crumple sound comes from the computer!
I think the justification for this is that, even if you have an external set of speakers plugged into your computer, you might have them off. Apple wants the Mac to still be able to beep at you to get your attention, even if your speakers are off (just like a PC can with its PC speaker.)
(Of course, you can reassign the "Alerts and Sound Effects" to your regular audio source, if you want to be able to mute them as well.)
Also, fun fact: if you don't plug in any external audio sources—for example, if you plug in an HDMI monitor to a Mac Mini that has no HDMI audio support, and don't plug in an audio-out cable—then all audio will come out of the internal speaker. Try it! (This was a common "thing" in computer labs back in the Power Mac days. You'd try to watch a YouTube video, but the computer would just have a CRT and no speakers attached. So you'd hear tinny sound from the tower!)
That being said, I have to say that the sound my apple laptop makes when it boots (which doesn't happen often; there is no wake-from-sleep sound) is oddly comforting.
I am actually disappointed it is being removed.