Hi Steven,
I wouldn't recommend this - this is not really safe. Typically, the permanent supply yellow wire to a car stereo is only designed to provide a few amps of power .... an active subwoofer will usually require a fair bit more power to run it properly.
At best, if you did this you'd probably find that the sub would keep cutting out ... at worst it would most likely keep blowing the fuse on the yellow supply wire (and even worse if the fuse value was too high, some physical overheating of the wire and physical damage could result!)
Even though it's a bit more work, connecting your sub directly to the battery as recommended using the right gauge cable (and correctly fused at the car battery end of the cable) is definitely the best plan - it's safe, and besides you will get the performance from the sub that you've paid for.
Cheers, hope this helps.
