Can I send packets received on LTM VIP to 2 Nodes at the same time?

Yes, but there are many nuances. In brief, for TCP, you can use a Sideband Connection to replicate the data in the CLIENT_DATA event. As a best practice, Sideband Connections should always go through a Virtual Server to reach the destination because a VS provides more fine-grained control. However, you must consider things like: what do I do if the backup node goes down? Do I store-and-forward (which is very complicated)? What do I do if the primary path fails (you can arrange your pool -- using priority group activation -- to handle this, but must then, in the iRule, make sure you don't replicate to yourself)?

Keep in mind that I'm talking about the TCP case here. If you are replicating UDP, things become somewhat easier, because, as long as you don't need fine-grained control, you can just use High Speed Logging.