ya, by grounding that wire your fans will come on whenever the key is turned on. if they dont, then you have a bad relay or bad fan motors. by doing this, you wont really hurt the motors, but you will probly shorten their life a little.
turn on your AC and see if the fan(s) come on. if they do, then you have a bad fan switch(temp sensor) just spend the extra $10-15 and get a new fan switch