Cutting part off would rarely kill any plant, to answer the question as simply as possible. All of the plants from my pics came from cuttings, except 1 mama of each kind, guess I didn't actually say that above. Coleus are known for being easy to propagate.
Tip pinching usually results in bifurcation at the tip, which is great, but won't necessarily encourage lower branches to grow as quickly as removing the lower leaves. This stuff works similarly on about any upright, branching plant.
This Datura plant bifurcated early on, when tip-pinched. Later removal of lower leaves has caused side branches to start growing.
This Begonia was a stem with a few leaves on it. I removed all of the leaves below the tip, now there are branches forming.
It's the same for Coleus. Removing the leaves lower on the stem would slow the rate at which it is getting taller as energy would be put into making the side branches. Just depends on if you want a bushy-looking thing, or more tall and airy like it is now.
The plants can survive as potted with roots, or as cuttings in water, that's what these are for. They provided this years' show (along with new ones I got this spring.) There wouldn't have been so many branches to cut off and save without selective pruning from the beginning, and all summer long. After growing outside all summer/fall, each planted cutting should have many new branches to cut, to repeat the process.
