EM waves fall off exponentially inside a conductor like saltwater. A 1 kHz wave has a skin depth of 8.75 meters, vs the Virginia class' 10m width. A signal from the front to the back of the submarine would be attenuated by 10 million times.
Note that this is in addition to the normal problems with antennas. Your home router transmits at <100 mW. Say you spent a ton of money and made a super sensitive receiver that could operate from 140m on the low SNR of your router. In order to receive the same power at 140m on 1 kHz, you would need a 1 megawatt transmitter. It would be dumping 60% of its power in the first 8.75 meters of water. Not quite enough to boil it, but not far off.
That's your first problem. The second problem is that the wavelength of a 1 kHz signal is 299.8 km. Antenna effectiveness also falls off exponentially with size, and the smallest antennas are maybe 10% of the wavelength. A 1 km antenna does not work well for 1 km, and even then you have to let out a buoy with a long cable- which is how current submarines do it.
The third problem is that if the drones are 10s of km or less away from the sub, there's no point. That means you know where the sub is. The problem is knowing where to aim active sonar or drop depth charges, not aiming.