there is tax avoidance and tax cheating in any taxation system. that wouldn't change, but there's also no reason to assume that the % of the gdp that passes untaxed currently would go up. if anything, the opposite is probable. countries with cultures that are largely accepting of tax fraud (the us is nothing close to this), rely a great deal on point of sale taxes because they're a generally easier to collect than are income taxes.
there's no reason to assume that people that don't cheat on their income taxes would suddenly start cheating. and while, steve dave may think he'd going to be smuggling in his new roof from canada, i think once he evaluates his travel costs, risk of significant fines and jail time, etc he'll probably settle for a new pair of shoes every couple of years.