He had a claim between 2001 and 2003, but he never cemented it. So, I'd lean no. He got robbed of a Hart in the Theodore year by a completely unethical Montreal voter who blatantly strategically voted for the Hart (left Iginla off his ballot, he gets any vote on that ballot he wins over Theodore). He won a Pearson and had 2 2nd place Hart finishes the 3 seasons before the lockout. Answering who the best player between 2001-02 and 2003-04 is almost impossible. Guys who had solid claims entering that era either had significant injury issues (Forsberg) or had a weird mid-career fall off (Jagr). For that 3 year span, you are basically left deciding between Forsberg, Iginla, Naslund, Brodeur, MSL, Pronger, Lidstrom, Sakic, and maybe a couple others.
Its strange in retrospect. Expected elite stars who were meant to replace the former greats all had injuries or fell off (Forsberg, Bure, Kariya, and Lindros). It created a power vacuum to an extent. People seriously discussed guys like Bertuzzi as the best player in the league.