Yes, JetPack will provide the x86_64 PC with CUDA and development tools which are also capable of cross-compile and deploy on a Jetson. If both desktop and Jetson have the same GPU architecture (Maxwell for a TX1 or the previous desktop generation, such as 960Ti, 660Ti, so on). With the same architecture there are still a few differences (due to running on ARMv8 and not being PCIe), but mostly the code will be the same. To learn for one will be almost directly transferrable to the other.
I have not used VNC, but others have said various virtual X servers do run on the Jetson and can be accessed through a PC in this manner. There is no virtual machine emulation of the Jetson itself (VM versus VNC) though I’ve seen questions about docker using GPU, but I have no experience with this and couldn’t tell you just how thorough it is. I do not know details of virtual box install, but there are some toolbox setup items within the local GUI environment already. It should work with the existing L4T (which is Ubuntu plus hardware drivers specific to the hardware…mostly Ubuntu documentation applies to a Jetson without modification).