I'm not familiar with the plants you mention, unless they are the ones whose leaves rapidly move away from you when touched. I saw some in Malaya. However, the plants well known for fixing nitrogen from the air and enriching the soil are legumes, belonging to the same group as peas, beans, alfalfa and clover. There are hundreds of them, and they all have similarly shaped flowers, though of many different colours.
They all have nodules on their roots which harbour the bacteria which do the actual nitrogen fixation. Like any other plant they also extract minerals from the soil, so the soil will be enriched with nitrogen but depleted in minerals. Farmers get round this difficulty by rotation of crops.
If the flowers of the plants you mention are similar in shape to the flowers of peas and beans they probably enrich the soil, and it is unlikely they remove enough minerals to harm your coconut palms. In England, farmers sometimes sow a legume like clover or alfalfa, then plough it back in so that the soil is enriched with nitrogen but not depleted in minerals. Perhaps you could do the same with your mimosa plants.
Most fertilisers contain nitrogen, and if yours contains anything else your mimosa will probably use a bit of it, but not enough to worry about. If your plants are indeed a kind of legume, that should enable you to use less fertiliser. If your touch-me-not plants have thorns on them, that's the only ill effect I can think of.