Going to build an immersion chiller. I have seen some that use a pump to recirculate wort to make the process faster. Why not just boil a spoon the last 15 minutes with your chiller and still the pot manually? Pros / Cons ?
If I understand your question correctly, you can absolutely use a spoon to whirlpool the wort as the immersion chiller is cooling. It will help it to cool faster than leaving the wort unstirred. The pump just makes the process easier. If you're going to build a chiller, personally I would suggest a counter-flow chiller.