Nodes checking their own VIP

Let's first concede that the client's request and the node's request are two completely separate things - different TCP sessions, different source addresses, etc. It's basically like persisting two external clients to the same node, which you can imagine wouldn't be the easiest thing to do. It could definitely be done though. For example, if you're willing to perhaps construct a relative URI path that the node would follow and indicate its persistence, that could be an option. Ultimately though, unless you need something from the VIP (some iRule logic for example), your best bet might be to simply trick the server into talking to itself directly via hosts file entry.