Can LTM be used to configure Active and Passive Servers?

Getting a stateful load balancer to do this will be "challenging". And it is worth noting that in all but a handful of scenarios (one maybe?) completely undesired.

To know whether it is even possible, we would need the Virtual config to see whether persistence is enabled and what profiles were in-use (possibly need their config also; iRules too?) to assess whether it was possible to use Performance Layer4 type Virtual.

Best case scenario, this might be possible by following the nPath configuration instructions (search on AskF5 should bring this up; worth noting that the name "nPath" has fallen out of favor, so it will commonly be referred to as DSR, or Direct Server Return) -- note that you aren't really doing nPath, but by configuring the F5 for nPath will allow it to not be stateful. This means each packet will be considered for load balancing individually, and that the F5 will no longer be stateful at_all outside of the response packet for a given egressed packet to the pool member (basically, you're configuring us as a dumb router, not a load balancer).

Coming back from the "how" to briefly visit on the "whether": Configuring an F5 Virtual to behave like a dumb L3 device is typically not possible and/or undesired in all but a gateway pool type scenario. The antithesis of this type of configuration would be a secure web shopping cart. As always, I highly recommend testing via a lab, or if needs be, via a "test" virtual that will impact only test traffic to ensure proper operation.