The a.c. adapter is used by the emonTx to calculate real power. For that you need the voltage, the current and crucially the phase relationship between them. If your emonTx doesn’t have an a.c. adapter, it can only guess the power based on assumptions - those being that the actual voltage is the same as the nominal voltage set in the sketch and the combined power factor of the load on the circuit you’re measuring is unity. Both those assumptions will almost certainly be wrong, by how much determines the amount of error in your readings.
What’s your electricity supply system - you haven’t given the country where you live but your IP address is Canada, so would I be right in guessing you have a single phase split supply (120 - 0 - 120 V)?
If you wanted, you could power all three emonTx’s from the 5 V d.c. USB supply (removing JP2 on all of them), and give all three the same output from the a.c. adapter to measure the voltage and to get a phase reference from. (But you must make sure you get all the polarities right.)
If you want to be really accurate (but it’s probably overkill), have two a.c. adapters, one on each leg, and try to arrange your c.t’s so that as best you can, one is dedicated to one leg and one to the other. You’d need to compromise with the 3rd emonTx and with the 240 V circuits.