I'm reading a book on openings and moving the pieces around is tedious, is learning to visualize entire games from notation achievable and practical?
Its achievable however not practical at your level. Go to
http://en.lichess.org/analysis and put the moves in as you go but do not have the engine on so you can figure out the stuff in the book yourself and do your own analysis.
It isn't achievable at any level. How many GMs do you know do their home prep lying in a bath, no they do it in front of chess board...go figure.
The goal of memorizing variations without chessboard is achievable, still it may be hard to recall that effort OTB unless you are a strong blindfold player.