This is a great question. It's interesting to think about how various treatments could affect plant growth, both positively and negatively. Once you start thinking about exactly how to test and measure the effect it can get pretty complicated!

The effect of caffeine on plants is not very well defined.

There is a lot of information (mostly anecdotal, which means not a well controlled experiment) about how coffee grounds can be used as a soil additive or in composting in general, but coffee grounds contain a lot more than just caffeine, so it can be hard to separate out the effects of just the caffeine. I actually compost my coffee grounds, but they get mixed in with a lot of other plant matter.

The coffee plant itself is pretty interesting - when it's leaves drop onto the soil, they can affect the pH and even inhibit growth of other plants around the coffee plant - but is it the caffeine in the leaves, something else, or a combination? You might be aware that our local pepper trees have this same capability by the way!

Luckily, with regard to your question, you can use purified caffeine and apply it to plants to monitor the effects, everything else being equal. Scientists have done this experiment, monitoring mainly germination (sprouting from the seed) and growth (cell division) at the root tips. They do a "dose response" test using various concentrations of caffeine and also "mock" (control) treatments for comparison. In almost all cases, caffeine, at a high enough level, tends to inhibit plant germination and growth. But, exact results depend on the plant species, how and when the caffeine is applied, and for how long. It is amazing how a simple question can turn into a really complicated investigation.