Yep, exactly what we faced. I didn't even push for whitelisting because we have 10 editors and maintaining their up-to-date IP's would be impossible much less getting GD to update them for me.
As I said we were actually very successful running our WP sites through their Windows hosting and were even able to use WinCache successfully with W3T. We just had other permission type nuances pop up. Our decision to move to VPS was solely based on site growth. We also found out that GoDaddy shared hosting only supported 400 concurrent connections to all sites in the account. That could have been an issue for use during certain times a year. The VPS was a no-brainer.