Hi Glenn,
Among the three type of destinations, URL and cookie destinations are real-time. S2S destinations can be set up to receive data either in "near real-time" (2-min delay) or in batches, depending on the destination.
Adobe Target (integrated via P&A) or legacy method can be considered real-time, along with other cookie or URL destinations.
To summarize, Profile merge rules will work with S2S (real-time), URL & cookie destinations.
Regards,
Harish