Gday,
I've been running the Axial AE-2 esc in my Tamiya MAN truck for approx 9 months with the C/C's 10 amp ext bec. I removed the esc from my Honcho as I changed it to brushless. The truck runs a 3s lipo with a 65t cralwer motor through a 3 speed shifting box.
I asked the same question on rccrawler and alot of the guys were doing it.
Pete
Axial link -
http://www.axialracing.com/blog_posts/787000000
They say it is fine to run 3s with the CC bec.