Your sources maybe talking about the efficiency with which electromagnetic radiation is produced compared with the dissipation of energy in the antenna.
All accelerating charges will produce electromagnetic waves. In your case an alternating current means that charges are being accelerated.
In general, the electromagnetic fields produced will have a number of terms in them, some of which will be important close to the antenna (known as the "near field"). These fields normally decay as $r^{-n}$, where $n\geq 2$ and become insignificant compared with other terms which become important far from the antenna (where far usually means many wavelengths of the radiation produced).
This "far field" or "radiation field" has field strengths which decays as $r^{-1}$ and have the general form $f(r-ct)$, corresponding to an electromagnetic wave.
When radiation is generated, it has a Poynting vector that carries a certain amount of power away from the antenna. Often, for a simple small wire loop, this radiation power is negligible compared with the Ohmic resistance losses in the wire itself.