Only if you are flashing. If you are doing something like cross compile, and you already have all of your software you need, then it won’t matter if the host PC has internet.
Technically, if you use command line flash and the flash software is present on the non-internet host PC, then you can also flash without the internet. The JetPack/SDK Manager software is just a front end to flashing and has the internet access content. If the content is present already, and you don’t use the GUI to flash, then you would still succeed. I would consider it a bit painful to never have internet on the host PC, but for some purposes you would not need the host PC to have internet access.
I would consider that your non-internet PC must have some sort of ethernet to the Jetson even if you ignore the internet.