Do I have to run cups to be able to add and print from a network printers ?
Yes. CUPS is what provides the server implementation. By closing down the cups service, You are essentially closing down the print server.
But I guess it is not mandatory to install cups on the client side?
Though I'm not really sure if its mandatory , it surely is going to make life a lot more difficult for you if you don't.
CUPS provides implementation for both, an IPP server as well as IPP client. The print server advertises its printers into the network, and any client on that network can thus talk to it using IPP requests.
To the computers on the network, the printers on the print server simply appear like IPP printers. As CUPS already provides implementation of an IPP client, it handles all the IPP requesting stuff for you.