We don’t have a dedicated print-server, is this necessary in order to use Princh?

No, it is not necessary.

However, we do recommend installing the Princh server software on a stable computer that isn’t used for daily interactions by staff or users. It is also possible to install Princh directly on the printers if they are "Google Cloud Print Ready".

We would be happy to look up your printer make/model to see if this is possible.