Can I use ADB wirelessly on an unrooted phone via SSH without a USB connection? My phone, an LG V10, is unrooted, something that I intend to fix. However, I appear to have a catch-22 ...

To put simply, it has a broken USB port, ergo the common recommendation of using USB debugging + 'adb tcpip 5555' to bootstrap a wireless adb connection seems to be a non-starter. My Warranty is non-existent. I reiterate for clarity's sake: it has not a single connection via ADB, it is not nor has it ever been rooted, and the bootloader is pure and virgin (i.e., locked). Would it be possible to send ADB commands to my phone via a non-root SSH connection (presumably with PuTTY and SSHDroid)?
You could use wireless ADB if your ROM has it, but you'd still need a wired connection for fastboot. So your only hope of rooting would rely on some hack over ADB, not the traditional unlock bootloader, flash recovery.

Unlock the developer setting: go to about phone in settings and tap the build number 7 times. Then go in there and look for an option for ADB over network.

You can also open up a terminal on the device, like you were talking about doing with SSH, but it would have even less ability to do anything useful (as far as rooting your phone,) than ADB.

If you do get it rooted, you might be able to install a custom recovery from the rooted system, at which point you'll be home free. You can download files and flash them from internal storage.