Can the ESRI app for the iPad consume regular web mapping services, or do I need to publish services for this app as Mobile project services?
I believe the Esri app for iOS can consume regular mapping services. The caveat is that your map services must be shared on ArcGIS.com. You would then search for your map services via Esri's app. There's a .pdf on arcgis.com with more info: using map services with iOS
Edit: Good discussion in Esri's iOS forum.