I'm trying to find a way to send a block placement to the server without actually placing a block. From what I've heard it would likely involve packets. So I want to ask, is it possible to manually make and send a block place packet to the server?

I think you should be able to simply return null in getStateForPlacement() (in custom block class), and you can get the information you want from there as well, otherwise you can also use EntityPlaceEvent that I don't think you will even need packets depend on what do you want to do.