The answer to the question, "Is it safe to connect a meter of wire between a digital output and ground?" is, "No." The resistance of a meter of #30 AWG wire, roughly equivalent to 0.05 mm2 - some really skinny wire - is about 1/3 ohm. That'll carry about 15A at 5V. From the ATmega328P datasheet, the absolute maximum rating for DC output current from a pin is 40 mA, which corresponds to a resistance of 125 ohms. If you connect the coil directly to the output, the pin won't actually delivere 15A; it'll deliver as much as it possibly can, and that's too much for it to deliver safely in the long term. It may not blow up in your face, but it'll never be quite the same, either.
Googling "poor man's NFC" yields a lot of hits, but they all seem to eventually lead here: http://jdesbonnet.blogspot.com/2011/05/arduino-to-android-io-on-cheap-aka-poor.html. The schematic shows a 120 ohm resistor in series with 30 turns of wire in a coil with diameter=1 cm, connected between pin 13 and GND, with a flyback diode across the coil. The photo, though, omits the resistor and diode, so the author's arduino is driving what amounts to a dead short circuit. He apparently thought that pin 13 already had a resistor in series for current-limiting for the LED, but the resistor is really in parallel with the pin. He says, "no harm done," which presumably means that his Arduino hasn't failed quite yet.
The code shows a bit rate of about 7 bps, limited by the Android's sample rate for its internal magnetometer. Bit transmission is coil on=1, coil off=0. The magnetometer's purpose appears to be for magnetic compass applications, so it's sensitive to DC fields. With this bit rate, I don't think that the system's RF characteristics are particularly important.
There's some code for the Android, to persuade it to decode magnetometer readings into serial data.
With the resistor installed on pin 13, the output current is still too high: 5V/120 ohms is close to 42 mA, and the LED draws nearly 7 mA, for a total of around 48 mA - still more than the absolute maximum. If you want to do this project, you'll want to beef up the resistor a bit, and drive the coil from a different pin. That may not develop enough magnetic field for reliable detection in the Android. If that's so, you'll want to buffer the output with a transistor, and you'll still want the flyback diode.