Of course! You can even make thousands of predictions per second. As you may already know, predictions are based on models that have been previously trained. BigML usually needs seconds to build the model and once the model is built, BigML is able to give predictions in a very short period of time, less than a second or in microseconds. This is because BigML models tend to be very lean and thus very fast.
You can get real time predictions with BigML in two ways: remote (you are connected to the BigML server and it gives you the predictions) or local (you are not connected to the BigML server and the predictions are made on your machine for FREE).