You can still redeem download codes for apps in the App Store in iTunes 12.7, even though the App Store itself has been removed from iTunes and the Mac (or PC). I found out when I plugged a code into iTunes just to see what happens, and it worked!
Redeem App Store Download Codes in iTunes
Not only did iTunes sans App Store accept the download code, the app auto-downloaded onto my iPad and iPhone, where I have autodownloads turned on.
I’m still annoyed as crap that Apple has removed our ability to browse and manage iOS apps on our Macs (or PCs), but at least we can deal with download codes.