Can I determine the rough frequency of an ac current by measuring the frequency of the electromagnetic radiation predominantly emitting from it?
Yes, you can definitely do that.

Since you're only looking for a signal, you don't need much coupling.  A coil held at right angle and close to the wire may be all you need for a pickup.

The ideal configuration is a toroidal core with the wire passing thru the loop, and the pickup wire wound around the toroid.  There are actually clip-on magnetic pickups for this purpose.  In that case, part of the magnetic core that goes around the wire to sense is movable.  The magnetic loop opens so that you can place it around the wire, then closes again to make good magnetic contact.  A bunch of turns of thin wire is wound around the stationary part of the magnetic core.  One place such devices are used is in strobe timing lights.  The magnetic pickup is clamped around a spark plug lead.

Current in the wire to be sensed causes a circular magentic field around it.  The magnetic core gives that field a nice place to go, thereby concentrating it.  The pickup wire is wound around a part of the magnetic core, acting like the secondary of a transformer.

You might be surprised what you can pick up with magnetic coupling.  Try winding a few 100 turns of magnet wire around a ferrite rod, then connect the two ends of the wire to the microphone input of a audio amplifier.  You'll be able to hear all kinds of things you might not expect as you move the coil close to anything with electric current in it.  Hold the coil to the earpiece of a telephone, and you can hear the whole conversation, for example.