Yes, you can stick the tube in and do something else. It takes a long time to drain a 125, so I use a pump to pump out the water. A couple time I have forgotten about it and pumped out all but 2-3 inches of water - while not very happy about it, the fish were fine. A good solution for that would be to time how long it takes to drain to where you want it, and set an alarm for future water changes.
Funny though, I've only ever overfilled one tank, but I had done it a few times. Gotta make sure you are focused when multitasking
And as I mentioned, removing the drain stopper will eliminate the threat of overflow at the sink.
As for sucking up fish - only my bichir has been dumb enough. Twice. Got stuck in the hose, but survived. Tough fish they are.
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