I have a domain with GoDaddy. In the DNS, I have the domain pointed to another hosting (websitebox.com). It is done by the A Record

Can I verify my site on Google using the GoDaddy option with the hosting not even being on Godaddy? Will it still pick up my site clicks and crawl items?

Quick backstory — I had my domain and hosting at GoDaddy for years. I wanted to switch to hosting at Websitebox. I first tried to use the WebsiteBox Nameservers and while it worked fine, when I would go into Webmaster Tools on Google, I added both my domain and the www. before my domain and Google was picking them up as TWO SEPARATE sites. When I had previously done this and had my domain and hosting on Godaddy, I’d only have to verify one and they were both picked up. Clearly linked.

Unfortunately, the new hosting company does not have any CNAME and wouldn’t add it on for me. So, Google was not able to see my domain and the www before my domain as one site when I used the Nameservers.

That’s what forced me to use the A Record — But I am unclear if Webmaster Tools will work correctly at all if that is verified with the domain only in the DNS with the A Record pointed elsewhere?