Well possibly,
but how are you going to tune the things, electrically small loops tend to have very narrow bandwidth and enormous circulating currents, so whatever you do needs to cope with lots of current and have very low losses.
You might find some of the ameteur work on the 73KHz band to be of interest.
Actually radiation efficiency tends to rise as the aerials get electrically bigger so you need less input power at higher frequency.
To give you a flavour, one of the US hams is working on 73KHz with a pair of 30m towers supporting a marconi aerial (T shaped centre fed wire fed against earth) brought to resonance with a dustbin sized variometer, 1,500W transmitter output gets him about 1W ERP!
TBH a mag loop down there is a scary (and massively expensive) concept lots of really butch copper, huge amounts of really scary high voltage capacitor and still almost all of your power goes up as heat.
You may wish to investigate 'Class E' power amplifiers for operation down there, 1 transistor rather then 4.
Now the sane way to do this.....
You are only looking to cover a room, correct?
If so, go for an 'induction loop' (A single turn of wire around the periphery of the room fed with a current mode drive of a few amps), pickup is a small coil. This is exactly the technology that used to be commonplace in cinemas for hearing aids with the switch for 'T' mode.
That gets you base to device in the room trivially, going the other way is harder as in that direction the small coil is transmitting and the noise contributions in the two cases are not symetrical.
Actually if I was doing it I would go for just putting in LED lighting and doing biphase modulation on the LED drivers (Simple, effective, fast) and forget about running VLF nearfield comms......
73 M0HCN.