You're going to have to take a look inside the furnace, where you should find the control board where all these wires terminate. Each terminal on the control board should be labeled, so just make a list of letters and colors. Then go back to the thermostat, and use the list to connect the wires to the proper terminals.
If you post the make and model (model number would also help) of the furnace, or a quality picture of the furnace wiring diagram (should be printed on the inside of the access panel), somebody may be able to offer a better answer.
FAN ON
When the FAN switch on the thermostat is switched to the ON position, the thermostat energizes the G terminal. This tells the furnace to turn the blower motor on. If the furnace is equipped with a multi-speed motor, the motor will typically be in HIGH speed when the G terminal is energized.
FAN AUTO
When the FAN switch on the thermostat is set to AUTO, the blower motor will only be turned on as needed.
Heating
When in heating mode, the furnace itself controls the blower. When the thermostat gets cold, it calls for heat by energizing the W terminal (If you're using a heat pump, the O and/or B terminals could be energized as well). When this happens, the furnace initiates the firing sequence. The furnace will try to fire up, and if successful, will turn the blower on after a timed delay (20-30 seconds typically). When in heating mode, the blower will typically run at a slower speed (LOW, MED LO).
Cooling
When in cooling mode, the furnace doesn't typically do much at all. When the thermostat is too hot, it usually energizes both the Y and G terminals (If you're using a heat pump, the O and/or B terminals could also be energized). The Y terminal tells the condensing unit (or heat pump) to turn on, while the G terminal tells the furnace to turn on the blower (again, at HIGH speed).
Risks of having FAN switch ON when in heating mode
There are two minor concerns with having the FAN switch ON when in heating mode, but both are more related to efficiency than anything else. First, remember that when in heating mode, the furnace has a delay before turning on the blower. This delay is important, as it allows the furnace to heat up before it starts blowing. If there's no delay, the furnace will start blowing cool air around, and could take longer to reach peak operating temperature.
The second concern is that when the FAN switch is ON, the blower is run at HIGH speed. Furnaces typically prefer a slower speed when in heating mode, to allow the air enough time to pick up heat. If the air moves through the furnace too quickly, it may not pick up enough heat. This could lead to cooler air temperature at the registers, and a potential overheating risk for the furnace.
Furnace heating elements; whether gas burners, electric elements, etc., typically don't vary their heat output. They're either on, or off. The furnace relies on the air moving through it to remove the heat it generates. If the heat is not removed, the furnace will overheat. There are safety devices built in to the furnace, that turn the heating element off if it overheats. However, these devices are there to handle exceptions, and are not to be used as temperature control devices.
tl;dr
Blowing around cold air, and overheating the furnace are the two risks I can think of.
Here's a very simple schematic of a thermostat, that might be helpful.
Best Answer
Can this be jumped safely, YES. Many furnace controls have the fan only option but as you found the wires did not extend to the thermostat. If you were able to use the 24v to pull in the fan relay and not activate the gas valve what you have done would not be a problem with normal low voltage thermostat wiring and would be hard to be unsafe at 24v.
Prior to installing any wiring I would get permission from the land lord. I have installed toggle switches on furnaces in the past for this same reason, to have a fan option, I did not consider pulling new 5/7 conductor wire to the thermostat as that would have doubled the cost of the job. The furnace was conveniently located, so it was no big deal to just flip the switch.