No, this is permethrin, a pyrethoid. Unfortunately, bedbugs are
technically able to be killed by pyrethoids, but only select populations and at high concentrations. Permethrin and other first generation pyrethoids are even less effective.
Foggers are also a touchy subject when it comes to bedbugs. Foggers tend to not get deep into crevices where bedbugs like to hide, and in many cases just drive them into deeper harborages, making them harder to get rid of. There are disagreeing opinions of course, but evidence is showing that they're ineffective in general, regardless of the pesticide used.
Check out this website for more information:
http://www.bedbugcentral.com/bedbugs101/topic.cfm/introduction