"My concern is whether or not W3TC actually does the job the CloudFlare plugin did and corrects those IP addresses?"
Yes, W3TC should take care of this for you. The easy way to check is to see what's happening at the WP comment level. Are you seeing our IPs or the ones of your visitors?
"If you're using DreamHost's CloudFlare integration (via your Panel) then you won't need the plugin for CloudFlare IP, as we have mod_cloudflare installed and it does the same thing."
The rep was trying to add that mod_cloudflare is installed on their servers, so this should also take care of the IP issue (signed up directly or through them).