Is it possible to download PSN games (PSVita, Vita-compatible PSP games and minis) via PC software (i.e. Media Go) and then connect Vita with the PC and transfer Vita-compatible games (either by using Media Go, Vita Content Manager Assistant or some other way)?
No, it's not possible to do so because PS-Vita games can only purchasable via a PS3 with a valid account. You can only transfer PSN games via a PS3 (this restriction is not applicable for media contents, videos, music etc.)
See here http://mediago.sony.com/enu/features/devices for all the devices that supports MediaGo to transfer content, and PS Vita is not listed.
You can login and purchase games from PC, but it just adds them to a download list - then you can transfer from the PS3 after they are downloaded, or go direct to vita.