In general, no it does not apply after death ([Az Nidbru vol. 8, 60](http://hebrewbooks.org/pdfpager.aspx?req=881&pgnum=140)).

See Chaim Byad Y.D. 125:48 who deduces as much from the wording of the Shulchan Aruch. He adds, however, that if one's father was his main teacher of Torah, he should refrain from sitting there for 12 months, out of honor for the Torah.

(However, if one's refraining from sitting in the father's place is meaningful in any way to the mother, that presents a new issue of kibud aim/honoring one's mother!)