Yes, a multimeter across the lead (red to tip, black to sleeve) will give you the output in millivolts as you play, but will fluctuate wildly with playing dynamics - the harder you hit, the greater the reading.
you could also put your multimeter across the hot and ground connections on your pickup(s) too - this time measure the dc resistance of the pickup. Generally a jazz bass pickup will be anywhere from 6.5 to 8 ohms, but I’ve seen some up at 11. There’s more to it than this, but it’s a good indicator that a pickup is either ‘hot’ or not.