No. The installation process will feel traditional, along with the location of installed files (per user direction).
The difference with FastStart installation process is that it downloads the necessary game files needed to play the game first, then moves on to lesser important game files to install.
This allows the game to be played within moments of the installation beginning, rather than waiting for the entirety of a traditional game installation to finish.
The game will continue to download in the background as you play. The quality of game play will not be affected by this process.