For many, many DDoS scenarios this does not work. The spurious packets may saturate an upstream ISP, causing that ISP to unilaterally apply a null route or block for all packets for the targeted origin IP. No CloudFlare packets would arrive at all.
If one is concerned about DDoS, one should work with their ISPs on the plan of action for various scenarios. Finding out their procedures when ones' hair is on fire is not fun.
It's not so much about changing the IP address, but moving the targeted system out from behind the clogged tube. Changing IP address may or may not do that.