While it's technically possible, we don't support mapping your domain by the method of pointing an A record to an IP address. Our IP addresses are subject to change and so there could be issues with your site displaying as expected down the road.
However, we do support adding custom DNS records into your account so that your email hosting with GoDaddy will keep working as expected.
These are the records used by GoDaddy users in the USA (which it looks like you are):
MX 0 smtp.secureserver.net.
MX 10 mailstore1.secureserver.net.
CNAME email email.secureserver.net.
CNAME mail pop.secureserver.net.
You'll want to go to Store -> Domains in your dashboard, and then click the link to "Edit DNS". Then paste in the records above and click the Save button.
It can take a couple hours to take effect, but then you can go ahead and change your name servers on GoDaddy's side and your mail will still work :-).
These are the name servers you'll need:
NS1.WORDPRESS.COM
NS2.WORDPRESS.COM
NS3.WORDPRESS.COM
These directions explain how to change your nameservers through GoDaddy:
http://support.godaddy.com/help/article/664/setting-nameservers-for-your-domain-names
Make sure to click the first bold link in the list on that page:
"Setting Nameservers for a Domain Name Registered with Us"