Not with many EVSE's. There are some that have built-in test/monitor displays, but they are in the minority.
If you have access to a clamp-on ac current meter and the ability to check the voltage as well, yes, you can figure it out easily: power=volts*amps. I put an inexpensive amp/volt meter on the input of mine, but the ammeter died, and it now only shows the voltage, so I can't use it. I guess I got what I paid for. There are certainly better quality ones available.
If you were using the OUC, Kill A Watt makes a plug in monitor you can buy for cheap on Amazon would work.