Not really. After 13....b6 14.Ne5 Bb7 15.Bh4 Black is going to have to disturb his kingside pawns anyway. By this point his position is already pretty bad.

Some comments from Lasker's tournament book.

After 6....Nbd7:

<The better system was 6....b6, followed by ...Bb7; or 6....c5 at once.>

After 7....c6:

<Blocking the diagonal of the QB, and loss of time as against ...c5.>

After 9....Qa5:

<Better at once ...Nb6 and ...Nbd5. The move actually [played] threatens nothing and defends nothing.>

After 13....h6:

<The bishop at c8 is now very badly placed; to 13....b6 14.Ne5 would be a disagreeable reply. 13....Bd7 should have been played, although Ne5 and Bh4 might have followed.>

Shredder points out that 17.e4 was a mistake, allowing the neat ...Nb4. After trading off White's KB, Black shouldn't be too badly off. But Lasker misses this opportunity.

After 20.Nxd7:

<White shows splendid judgment of position, by playing for two Bishops; this gives him a lasting superiority.>

After 24.e5:

<To meet 24....Ng5 by 25.f6.>

After 32....Ne6:

<If 32....Nh7, then 33.e6.>

After 34....Qg4:

<A "swindle." Owing to White's two Bishops and the strong passed Pawn, Black can defend himself only by counter attack.>

After 37.Rd3:

<‘The story is told that during the course of his game with Emanuel Lasker (the world champion) in the St Petersburg tournament of 1909, Chotimirsky read a Japanese translation of Thus Spake Zarathustra. Legend has it that the world champion was so incensed at the young man’s studied insolence that he lost the game. Whatever the cause of his defeat, Lasker was singularly reticent about this encounter.’>

http://www.chesshistory.com/winter/...