Does AC current produce EM waves?

You are right, the transmission of AC does in fact produce EM waves around it. These waves are indeed sinusoidal, but we do not bother about the power losses until we start sending radio signals via these wires because, until the frequency is much higher than radio waves, the energy lost is extremely small and hence negligible. See

Ordinary electrical cables suffice to carry low frequency AC, such as mains power, which reverses direction 50 to 60 times per second. However, they cannot be used to carry currents in the radio frequency range or higher, which reverse direction millions to billions of times per second, because the energy tends to radiate off the cable as radio waves, causing power losses.
(SOURCE : http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Transmission_line.html)

Even for radio signals we do not lose a lot of energy but it start making a significant effect thereafter, this is why we do not consider the losses encountered as EM wave transmission while handling single/low frequency AC circuits.

I think the issue is that while a powerline does produce fluctuating EM fields, that is not the same as EM "waves" or radiation. This distinction is summarized on the wikipedia page about near vs far fields. In short, the two wires on a powerline have opposite phase, so that two adjacent pieces form an oscillating dipole, and we'd expect dipole radiation to escape from the powerline. However, the all these dipoles interfere with one another (because they are out of phase) and so the field that escapes to infinity is very small.

On the other hand, powerlines induce currents in the ground and nearby water, and this is a source of major losses. This is one reason powerlines are rarely buried, other than cost. Also, undersea power lines are often DC for this reason.