James -
AFAIK, you can still check to see what processes are running using standard UNIX C-style system calls (i.e., think sysctl). However, it should be noted, that wouldn't be approved if you were submitting to the store.
Check out the document below to see what the various modes of background operation are. Depending on the permission(s) you request, you may find the iOS SDK will refuse to perform some other unsupported behavior (such as system-level calls), but it's work a shot, I suppose, if someone is paying you to do it!
For example, see "Fetching Small Amounts of Content Opportunistically". You might be able to get your task scheduled in the background via that permission, and use it to sample the processes running.
As far as getting the continuous ability to run a spyware task to look at processes running on a device, you can't do that without rooting the OS. (One more reason to own an iPhone!)
Thanks,
Mark