Hey Tyson - at this time no, this map visual does not support ArcGIS Enterprise / connections to Portal for ArcGIS. It's a hot topic of discussion here at Esri, though, and we're working through some technical challenges to see if it's possible to provide ArcGIS Enterprise support.
One of the technical challenges is supporting secure connections from Power BI back to ArcGIS Enterprise. The underlying technology (chromium) that Power BI provides for visuals doesn't support all authentication types. It would be great if you (and anyone else requesting ArcGIS Enterprise support) could email me information about how you authenticate to ArcGIS Enterprise. This would help us understand if what we can build will actually work for those of you who want this feature. You can reach me at s b a l l @ e s r i . c o m - thanks!