This build works acceptably for ARAM, but has been tried and mostly abandoned in Summoner's Rift. It's extremely based on over-time sustain, but it comes at the cost of relatively low impact in an actual fight. That's perfectly fine in an environment heavily based around poke and where the enemies can't do anything except throw themselves against you, but it faces huge problems when enemies can flank you, have better ways to hard-engage on you, or can force objectives so that you won't get use out of over-time sustain.
Basically, it's an acceptable build, but it does have massive weaknesses that can be exploited easily, and those keep it from being a good build for Summoner's Rift.