The texture will remain, actually, at least using most types of potato mashers I've seen. With something like beans, you cant turn them in to mush no matter how hard you use the tool. You're mainly just breaking the beans up in to smaller chunks.

In bean dishes, I find it works really well to 'mash' about half the beans, leaving the others intact. This results in the bean fragments better able to absorb whatever flavors and spices you have in the dish, producing a more complex dish, with an interesting 'mix' of bean types and textures.