I don't see why it won't be possible, but your question is a bit odd...
You can't use a gif on a domain... the domain must be attributed to a hosting plan, and inside that hosting plan you will have to create a web page that will contain the animated gif file that you are referring to.
I'm having the same problem. In the help topics it says you can upload a .jpg .png .gif but when I upload a gif it appears as a static image. I'm on a monthly plan which I assume includes hosting as I published the page (for my view) and it's live so my plan must include hosting
I'm new to GoDaddy web builder. A few months ago I got rid of my phone (to be less contactable) which means I cannot reach out to GoDaddy directly for support
Just so you all know. I've spoken to support and the new web builder does not support gif files. How crazy is that?
I bought the new web builder, finished my website within 48hrs, then needed to call support to fix the gif issue I was having. I was told that the new web builder does not support gif files and there are no plans to support it in the near future. I was then told I could buy web builder 7 as that does support gif. But, I would not be credited for the new web builder and would need to buy version 7 too. It was frustrating, but I remained polite and asked how would you feel in my shoes? The support worker said he doesn't think like me and he'd be happy to pay twice.
So, in a nutshell. If you want to include a gif on your website, you have to buy the new version, then call support when you have a problem with the gif, then be sold an older version (which isn't viewable when making your initial purchase). When you politely show your frustration you'll be told they don't think like you, like you're some kind of meanie who should be happy to pay twice. Then after all that, and you pay twice (because you need a gif on the website), you have to restart making the website from scratch as the template you used in the new web builder is not available in version 7. Wasting our time, and our money, and get made to feel like crap on the phone.
Great job GoDaddy, you've excelled yourselves!