Well the D1s have a built-in Photocell/IR-slave, so they should trigger when a flash is fired - regardless what source the flash comes from.
But I don't know if the Sunpak can be used as a slave device - it can certainly be the master flash and trigger the D1s.
Honestly I'm not sure if it's feasible though, the sunpak ring flash won't be very powerful, especially as large distances. These speedlight-types are for close-up and macro work and lose their efficiency quickly over a bigger distance. So most likely your Profoto heads will be way too powerful, depends on what you have in mind....
I have worked with a ring-flash head on the Elinchrom Ranger RX 1100Ws but I never mixed it with other heads or with profoto for that matter..