The stainless steel parts are in direct contact with zinc-coated carbon steel? The parts will be exposed to a hostile, damp environment? You can anticipate galvanic corrosion among your components, and the expected lifetime would be short.
The change in lifetime versus using galvanized fasteners to galvanized sheet will be fairly modest because typically with fasteners the area of the fastener is small compared to the area of the object it fastens to. Secondly, the stainless fastener will be passive and very little corrosion current can be generated by it. The surrounding zinc surface coating is already sacrificial to its iron substrate, so I predict very little life shortening of the system.
I agree with this insight of CoryPad. All the harm done by the galvanic couple will be concentrated at the contact between the stainless and the zinc. If this point is structurally critical, it's a inadvisable materials combination and galvanized fasteners should be used.
Stainless fasteners for use on Galv. connections are O.K., as long as the total fastener is SS & not a SS bolt w/ a Galv. Nut. Any joint corrosion will be the Galv. parts, not the SS items. Of particular note are Cooling tower bases & structures that are continually damp. These will hold up maybe 10 to 15 years w/o corrosion, if the galv. application is not disturbed, IE: field welding and then zinc coating. Hope this helps.
The other thing that you see done is to use non-metalic or coated washers. This greatly reduces the galvanic issues. Stay with SS bolt and nuts, but isolate them from direct contact with the Zn.
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Corrosion, every where, all the time.
Manage it or it will manage you.