The Capital Blvd. North Corridor Study (which is still ongoing) seems to go much farther -and their last public presentation talked about median-running BRT-exclusive lanes with inline stations at key intersections.
The City made an ArcGIS StoryMap that goes into all the neat details about that corridor plan, too (first posted here by @thehappysmith). They’ve been silent about their progress since then, though, and their last sign of life I could find is this discussion on bikeways around that corridor back in February.
If the BRT-related suggestion survives and makes it onto the adopted study report, then NCDOT would have to put in a significant amount of money into these upgrades. I bet GoRaleigh would run BRT to North Hills first like @pierretong suggested, and treat the Capital extension as a separate branch line. Maybe this could be a part of a package of BRT extensions, alongside the RTP and Clayton ideas?