As long as you do not use any hard-coded IDs in the integration, there should not be any need to use it with an account from another site. The integration acts on the behalve of the authrizing user, so if you sign in with the account from org A, than it it for that site, if you use an account from another org, than it should work there.
If you have multiple sites in your organization, then you need to utilize the siteUrl parameter which is available for most of the meeting API endpoints. For non-meeting endpoints, the site does not matter, therefore no need to provide it.
