Whew, thats a tough one. I possibly *could* but I wouldn't recommend it.
First of all, to run a P4 with utmost stability, you should use the extra 4-pin square power connector (its specially made for P4's, it's part of the ATX 2.03 spec I believe) on the power supply, which I doubt that PS has. Even so 180W probably too low. Now some motherboard manufacturers make connectors on the motherboards that use a regular 4-pin HDD connector to get that extra power (like the ASUS "EZ-Plug" on ASUS motherboards, but this is only done for convenience and is meant for higher powered PSes than 180W.
Now both Intel and AMD recommend 300W power supplies for their newest and greatest chips, with 250W being the realistic cutoff point. I recently went from a generic 300W power supply to an Enermax 350W one and it helped me with my overclock a little bit.
So I'm sorry to say but I definately would not recommend running a new P4 or Athlon with anything less than 250W, or maybe a really nice 230W power supply with very few devices.
Look for a good 300-350W power supply and it should run fine.