It doesnโt make a difference to CoreSpotlight whether the data is present on the device or not. In order to index data, it has to pass through the device, but you could easily choose to index stuff you pull down from the network and then discard.
Itโs up to your app to cope with pulling down the appropriate data when provided with a search result though.
I would expect that in most cases, if you have completely remote data, the search functionality would be server-side too. The exception being if when you start the app, it downloads all the personal data and caches it locally.
Apple provide some pretty good example guidelines for what to use different aspects of iOS search for in different situations: