The method of integration we use for HubSpot is to periodically (daily/hourly) 'cache' the contact data which would then be available to identify the caller. This 'cached' contact data is used to identify callers therefore would not be 'live' data.
If the integration supports caching, please note that cached integrations support up to 30,000 contacts. The live mode method would need to be used for larger directories. The performance will then be determined by a number of additional factors including network speed and application API specification.