When data ingested in AEP, it would be available in Data lake and real-time customer profile . As soon as data available in real-time customer profile , profile can be searchable based on identity namespace and data will be reflected in profile.
I assume you are ingesting data via streaming HTTP source API call. If yes, data travels via pipeline to real-time customer profile within 1 min and then Data Lake/datasets within 15 min. In this case, search profile with an identity namespace, data would be reflected in the unified profile less than a minute.
If data inserted via batch, first data flows to data lake/datasets from there real-time customer profile. In this case data would be NOT reflect in the profile immediately, takes couple of minutes.
Check below documentation : https://experienceleague.adobe.com/docs/blueprints-learn/architecture/architecture-overview/platform-data-flow.html?lang=en
To answer your question. Yes ,real time customer profile is really real time 😊 it depends on how you are ingesting data .