Can I connect a portable washer to the cold water connection?

I have a pull out spout type faucet. While I CAN remove the head, I've read that you should not connect a portable washer to this variety of faucet, and I don't really want to replace a brand new $300 faucet! Could I just attach the water intake for the washer UNDER the sink, where the faucet supply lines connect to the water?