What kind of unit? Window, ductless, CAC (split/package system), etc.
Most air handlers (sometimes called "the furnace" by homeowners) will have the blower FLA (full load amperes) listed on the nameplate. It's also important to note if this motor is 120V or 240V as well. Multiply this value by the voltage and multiply that again by .75. (the average power factor at full load) The result is the power draw in watts.
Most people are billed by the kilowatt/hour. That is 1000 watts for one hour = one billing unit of electricity. Your electric supplier or "diesel generator man" can tell you what exactly you are paying per kWh as well.
Let's use an example of a typical four ton air handler with a 3/4hp indoor fan motor. The nameplate says 5.8 FLA and the voltage is 230V. 5.8*230*.75=1000.5. That's very close to 1kW and your calculations are approximate as you don't know the exact power factor, feed voltage AND actual amperage draw. Some motors may only be drawing 90% of FLA because of coil/filter restriction, etc. If you MUST have exact amperage and voltage you can borrow an amprobe and get these values.
In any case a 1kW load is easy to use as it will use exactly 24 units per day if you run the motor 24/7.

Multiply that by your actual rate and you will see it adds up.
Newer units also use variable speed fans and it would be assumed that placing the fan ON/OFF/AUTO switch in the ON position runs the motor at full speed. Unless there is a specific reason why you need to have this motor running it's best to leave your thermostat in the AUTO position.
As far as service life running the motor continuously most definitely will reduce its operating lifetime. If the bearings are not sealed they will need to be lubricated at more frequent intervals. This can be a PIA (although not as bad as replacing the motor!). Additionally with the fan on 24/7 the filter will need to be changed/cleaned more frequently as well. Dust may become more apparent on return grilles and/or need to be cleaned with greater frequency.
All in all it does not sound like it's worth it.