Not necessarily, if it is from Alby -> Alby then it is essentially also just a db update.
But the latency comes from several steps, that can take long even if no "real" LN payment happens:

• Fetch LN invoice over HTTP
• Dispatch invoice over websocket
• invoice gets paid
• Zap Nostr event gets published to relays
• Zap Nostr event is received by your phone