Yes, SPG Plat can access the second floor lounge. Also the "heavenly bed" is light years ahead of the Sheraton beds in my opinion. Westin is the way to go, no comparison.

The only down side is that it's a good 5 min. walk to MRT rather than the MRT being right outside of Sheraton, and also the MRT line near Westin is not a line that goes through major commercial centers, so you need to make connections to other lines. The Sheraton MRT line (Blue line) is the main line that links all of the major Taipei commercial centers together (such as Taipei 101 area, Taipei City Hall station.)