Righto!! He're a handful of questions to ponder......
Are search and destroy programs such as SUPERAntiSpyware and Malwarebytes, able to be run through a system that already has other anti-virus and anti-malware programs like avast!, Avira AntiVir, SpywareBlaster, Ad-Adware 2008, and SpyBot etc. etc., running in full and active mode?
Yes. [I use the paid version of Superantispyware.]
Is there a need to disable the active anti-virus/anti-malware, before running any scans by those programs highlighted above?
No.
Should the scans be done with the PC/Laptop disconnected from the Internet?
Yes. [I always disconnect my laptop.]