I think if he has a similarly big flaw in a vital aspect of his game he probably will. For instance Gomes (of Spurs) was pretty much ridiculed as a goal keeper. I agree that foreign players are subject to more critisim than UK ones, but even a UK keeper who was poor would get a bad press look at Rob Green - in the same way other fans and the press are calling David De Gea "De Flapper", David James was called "Calamity James". If the keepers improve and eliminate the weaknesses then the critisim will ebb away - by 2005 James had been a bit more stable and the critisim went, similarly with Erik Thorsvedt at Tottenham, poor at first but a decent keeper by the early 1990s. Even this season I can remeber Gary Neville saying he'd "never seen Julio Cesar make a proper save" a few weeks ago, but now most journalists and fans recognise him as the in form keeper in the league. Some top class foreign keepers don't really get that much critisim at all (Van Der Saar, Howard, Given (until he got too old and his reflexes went in the last 2-3 years), Schmeicel). Foreign keepers who've never played in England are still by and large recognised as top players (e.g. Buffon, Oliver Kahn).
De Gea is very good at shot stopping especially from distance, but he still can't deal with crosses into his box and doesnt command his area very well. In some ways he's unlucky as, in most outfield positions, players can afford to have an area of weakness as the formation or starting 11 can be re-jigged. For instance Cafu was a sensational wing back, but defending wasnt't his best skill, however Milan (and to a lesser extent Roma with Aldair) were able to play experienced, positionally clever, center backs and strong defensive midfielders to counter act this. Goalkeepers just dont have this option as they are the last line of defense.