I deleted PHP via SSH using yum as an update would not work, but it seems to have also removed Plesk - I presume because it is dependent upon PHP?
Is it possible to restore or reinstall Plesk via SSH?
Sure, I mean you can do almost anything via SSH. For your needs, just do
Although I think it would ultimately be better to shell into the OS and do the Yum install.
If you new to Linux and Plesk, I would rather not recommend you installing Plesk by yum. Plesk autoinstaller does several extra configuration steps which yum will not perform, so even if installed, you won't be able to access Plesk until you do all these configurations.
I can suggest two options
Hope something of that can repair your installation.