Yes, it will, but in a different way than one might imagine. In the Earth's oceans it is definitely impossible.
From the phase diagram of water, one can see that assuming a constant temperature of 300 K, water becomes solid ice VI at about 1 GPa. This kind of pressure would be encountered at a depth of about 100 km (actually a bit less because of the increasing density). By comparing this pressure to the bulk modulus of water (about 2.2 GPa) we can conclude that at 1 GPa the density of water will be about 1500 $\mathrm{kg m^{-3}}$. So if we had a (sweetwater) ocean deep enough, the penny eventually comes to rest at this depth on a layer of solid ice, even though its density will be less than that of the penny.
At the same time, we must not forget the penny itself is compressible. However, for zinc, bulk modulus is about 55 GPa, so at 1 GPa the change in volume will be only about 2%, which can be neglected.
However, if we insist on having liquid water, we can also increase the temperature. 815
According to the diagram, at the critical temperature of 650 K we can continue increasing the pressure to about 15 GPa before water solidifies. This looks promising, but the bulk modulus of water is not constant. It increases with pressure, so it is probably still not possible to reach the density of zinc, 7000 $\mathrm{kgm^{-3}}$. So with liquid water it still is not possible.
At even higher temperatures, water goes supercritical. If we find a larger phase diagram, at 1000 K it should be possible to have supercritical water at some 50 GPa, which should theoretically be enough to compress the water while keeping the penny relatively uncompressed. Unfortunately, since bulk moduli are not constant, it is likely that this still will not be enough.
We should also remember that the melting point of zinc is fairly low at standard pressure. Fortunately it gets much higher with increasing pressure, and at 50 GPa it is already above 2500 K.
I am not able to find any experimental data for this extreme region, but it still seems remotely possible that somewhere there actually is a combination of temperature and pressure at which water is supercritical, zinc does not melt yet and the ratio of compressibilities remains low enough that the penny might remain afloat. 815