Thank you for your feature request.
You should be able to disable all alarms (email notifications + "dashboard issues" etc.) by disabling the monitors for those clients. By doing this, you'd still be able to see your clients in the MSP interface without seeing any issues that may confuse your service desk.. You could furthermore ad "ignore" (or similar) to their client names, in order to clearly mark which clients your service desk should steer clear of.
I agree that filters/views would probably solve this in a cleaner way, but I hope my suggestions help.