What impact does the Account ID argument to Site.createPortalUser have?

In and of itself, the AccountId has no impact on the access rights of the User until permission sets or sharing rules are applied.

The basic profile of a PortalUser isn't dependent on the AccountId. It's the license type that impacts what the profile will have access to. Obviously, an AccountId is required for a customer Portal. If you're talking about a Partner Portal, the AccountId will affect which child Accounts the user will have access to, which again is a matter of sharing rules and permission sets that are subject to what the base license allows that type of portal license or community user license user to have access to.

The only exception to this that I can think of would be where there are other licenses which can be used that a common AccountId are applied to. For example, in some sites, an org might apply a guest user license to a common "dummy account" and restrict the permissions of those users compared to the users who have a full license to use that portal, site or community. But again, that's really a matter of permissions that have been assigned to a particular profile and/or user. In the example cited, that's a different profile than the primary profile assigned to "registered" users; thus the reasons for the limitations and restrictions placed on it.

Depending on the type of "Portal", "site" or "community" license you have, sharing contact information between Users from the same account may or may not be a simple thing to do. Each license is different and the sharing models can vary significantly. Having an account in common would simply be one of the criteria used as part of the sharing rules used to grant the permission.