Definitely not possible
no access over computer keyboard if your device has not been jailbroken
with openssh preinstalled before
You can use iCloud Backup on recognized WIFI networks to sync automatically
if previously enabled, though
If your iPhone gets recognized by iTunes on your Mac, you are still good to go for a screen replacement considering it not being as expensive as a data loss, nor the lightning keyboard and more important you don't lose your app tokens, for example some banking apps, app-related logins, authenticator apps, etc.