To answer your question, no.
SAS software that accounts for the study design of complex sample surveys like the design-based PROC SURVEYLOGISTIC is not based on maximum likelihoood estimation. Thus, Firth's method is inapplicable in this procedure. However, some have attempted to mimic this design-based analysis of complex sample surveys using model-based methods like generalized linear mixed models in PROC GLIMMIX.
Since SAS code to replicate Firth's method is available at
http://cemsiis.meduniwein.ac.at/kb/wf/software/statistische-software/fllogistf/,
you may be able to adapt this code to a PROC GLIMMIX model for analyzing complex sample surveys.