Hi Seamless,
Yes, this is possible! In fact, at our office we have the same set-up; Our domains are registered with GoDaddy, and we use a Google Apps account for our email addresses.
First, you will need to sign up for a Free Google Apps account with the domain name you want to use.
Second, you will need to update the MX records in your GoDaddy.com account. This used to be a painful, manual process, but GoDaddy has created a tool that changes your records automatically. Visit this URL: https://www.godaddy.com/gdshop/google/gmail_login.asp and log-in with your GoDaddy.com account. Enter the domain name you want to use with Google Apps. Keep in mind that it can take up to 48 hours for your MX records to update.
Third, you will want to log-in to your Google Apps Control panel (http://google.com/a/YOURDOMAIN.com), where they will require that you verify your domain name. There are a couple of ways you can do this, but we recommend creating a text record.
To create a text record, log-in to your GoDaddy.com account. In the left-nav, there is a section called "My Products." Find Domain Manager and click on this. You will be taken to a screen with a list of all of your registered domain names. Click on the domain name you want to add a text record to. Find the section labeled "DNS Manager" and click LAUNCH. Find the heading TXT (Text) and click the QUICK ADD button. Copy and paste the text record provided by Google Apps into this field.
Keep in mind, it can take up to 48 hours for a text record to propogate. Once Google Apps has confirmed you own the domain name, then you can log back into your Google Apps Control panel (http://google.com/a/YOURDOMAIN.com) and activate the email feature.
I hope this helps you out!! Please let me know if you have ANY questions!
Thanks,
April Coburn
ChooseWhat Staff