Yes. Six Sigma is completely supportive of your previous CMMI work.
Exactly how you integrate the two models will differ slightly (but only
slightly) depending upon the timing of their implementation. For those
with a longer CMMI history (most likely dating back to the SW-CMM),
the introduction of Six Sigma will broaden the organizational standard
process in use to include a broader array of business and strategic
improvement projects. The tailoring guidelines used by projects to adapt
the organizatioonal standard process will need some adjustment to this
broader scope, perhaps adding a new step to decide if the broader Six
Sigma models are relevent to a project or simply the older and narrower
traditional software or systems engineering lifecycle.
For those of you with a shorter CMMI history, you'll likely find that
the introduction of Six Sigma is a big help in clarifying some of the
quantitative vs. statistical distinctions that crop up so often in interpreting
some of the CMMI measurement requirements, particularly among the higher
maturity practice areas. If basic CMMI-derived measures are in place
within the CMMI program, Six Sigma will take advantage of those measures
to identify and control change and improvement initiatives. Without
your CMMI foundation, your Six Sigma initiative would have to start
building quantitative capabilities into your organization from the ground
up. The synergy between these CMMI and Six Sigma disciplines will provide
you with effective economies of scale as you broaden your process programs
beyond CMMI to include Six Sigma.