The answer to your question depends on which particular organization’s rules you are asking about. For example, some 3-gun competitions may allow pistol grip shotguns while others may not. So it just comes down to check with the specific organisation that you’re interested in competing with.
Generally speaking, a pistol grip shotgun would be classified as an “Other Gun” under most 3-gun rulesets. This simply means that it doesn’t fit into any of the other defined categories (pistol, rifle, or shotgun). Each match generally has a specific list of firearms that are allowed in each category, and anything that doesn’t fit into one of those categories is considered an Other Gun.
That said, there are usually provisions in place that allow competitors to use another gun if they don’t have a suitable firearm in one of the other categories. For example, a competitor might be allowed to use a pistol grip shotgun in the shotgun category if they don’t have a traditional shotgun that meets the requirements. Again, it just depends on the particular organization’s rules.