The problem the OP is complaining about is "background scanning", not "real time scanning". Most AV products will allow you to disable "real time scanning" (scanning files as they are fetched and/or downloaded). (Often this is necessary to install certain software packages.)
But I know of no product that will allow you to disable "background scanning" -- what Norton is talking about when it says "Norton 360 is currently performing background tasks while your system is idle," eg. At most they allow you to "schedule" the start of the scan, and perhaps adjust it's "priority".
"Real time scanning" can be an issue because it prevents installing some software packages, or because, on very slow, resource-constrained systems, it makes many operations run slowly(precisely because it's NOT in the "background", but in the application critical path). However, on most systems, most of the time, the "real time scanning" of a good-quality AV product causes no noticeable performance impact.
"Background scanning" is supposed to run in "background", using only "spare" CPU cycles, etc. However, on many (Windows) systems the scanning seriously pollutes the main store and disk management mechanisms, hogging RAM, creating long I/O queues, etc. Thus, even if the scanner "pauses" because it recognizes that the computer is no longer "sleeping" and is being actively used, it may take from a few tens of seconds to several minutes for the queues to empty and normal operation resume. During this time the disk activity light will generally be on solid.
There is some difference in the behavior of different AV packages in this regard. In my experience, Norton is halfway well-behaved (only pollutes the system moderately), while McAfee doesn't "pause" nicely when you're using the system (and thus causes the system to behave poorly for the roughly 24 hours required to scan even a relatively small 200G laptop system), and Kaspersky, though it seems to "pause" at least some of the time, leaves the system badly polluted.
So, to answer the OP's original question, I don't believe that there's any major AV product (at least not Norton, McAfee, or Kaspersky, last I checked) that allows you to disable background scanning. You could try killing the scanner task, but that might also disable other AV activities (or simply cause them to hang, hanging the system), or the AV software may very likely restart the task. And removing the AV product from the startup list would likely leave you totally unprotected.