Answer
No, it is not possible to integrate Google Street View in ArcMap as the functionality is currently not supported.
However, ArcMap layers can be converted into Keyhole Markup Language (KML/KMZ) files, and imported into Google Earth. Data from Google Earth or Google Maps can also be loaded into ArcMap via the conversion of KML/KMZ files into layers. However, the data from Google Earth or Google Map can only be loaded into ArcMap if the KML/KMZ file is version 2.0 or older. Refer to the links below on how to convert layers in KML/KMZ files and vice versa.
ArcGIS Help: KML To Layer (Conversion)
ArcGIS Help: Layer To KML (Conversion)
Note:
There is a third-party widget, called the Google Street View Widget, that creates a web application that integrates Google Street View with ArcGIS for Desktop via ArcGIS Viewer for Flex. However, since this widget belongs to a third party, Esri does not support its use.