They do suck up a fair amount of nutrient, they're particularly big users of nitrogen, phosphorus and sulphur.
I've never really thought of them as an acidifier though. If it's a long term pasture that will self sow I would periodically be applying nutrients to keep it going well. The cheapest option is urea and superphosphate. You may want to apply some traces every now and then but that would depend on the fertility of your soil.
On the note of acidity, pure legumes can do this. If you have a straight clover or lucerne/alfalfa plot for example, the excess nitrogen they fix can lead to acidification. You can address this by either liming or planting a grass to take up the excess. Bear in mind liming requires incorporation, top dressing has little impact because lime is so immobile.