I want to add a site to gmb but am thinking that if I register as a local business that Google will stop showing me in global serps. Can you be local and still show in national or global seeps? Thanks
I work with a site that has a local listing and global traffic. Google will still show you in the global serp and show your business in the map pack for regional searches. Something to consider is that your local page may show up in a larger region than what you think is "local" and that the ratings, reviews and status (open/closed) for that location could impact the results of your branded searches.
I've used VPNs to gauge how far Google thought that listing should be displayed on a branded query. The local business really only got traffic from NY and Canada yet, Google showed the business page on a branded query to most of the US east coast.
About 10% of the site traffic is from NY and Canada.