The issue of screws versus nails seems to come up frequently on this forum. The shear strength of a nail or a screw depends on the strength of the metal (usually steel, but could be aluminum, brass, copper, galvanized, or ceramic), and the thickness of the shaft. Some people believe that screws are not as strong in shear as nails, but this is based on a misunderstanding of the properties of screws and nails.
Nail diameter is measured along the shank of the nail. Screw diameter for purposes of computing shear is the root diameter of the screw, i.e. the shank of the screw, and DOES NOT include the threads. So a screw which has a root diameter of 1/8 inch is just as strong in shear as a nail with a shank diameter of 1/8 inch, assuming they are made of the same material.
Screws have greater pullout resistance, because a screw resists pullout by mechanical connection to the wood, whereas a nail resists solely by friction. Depending on the type of connection, your connector may be subject to shear, pullout, or both. In my experience as a structural engineer, screws are as good or better as fasteners than nails, provided they are properly sized and installed. I was not aware that they are PROHIBITED by code, however building codes typically include nailing schedules for connecting framing members, but not screw schedules, so perhaps this could be interpreted to mean that since no schedule is provided, you cannot use screws, unless of course specified by a professional engineer as part of the plan.
That said, a quick review of current literature on attaching framing members will provide you with many examples of connection details using screws. Recent research from Florida discusses attachment of plywood sheathing to roof rafters, and recommends either screws or special ring shank staples (ring shank nails and staples have extra pullout resistance due to the mechanical bond of the rings).
I have specified screws for many structural projects, they work fine, but there are a few things to be careful of. First of all, the two elements to be joined must be correctly aligned before you drive the screw, since screwing will not cinch up pieces (unlike nails). This is often best achieved by clamping the two pieces together, then driving the first screw. Once you get one in, the clamp can typically be removed. If you cannot clamp the pieces, you need to bore an oversized hole through the first piece, then drive the first screw. As long as the hole in the first piece is larger than the thread diameter, but smaller than the head of the screw, the pieces will cinch together. As before, once the pieces are cinched, you can drive the remaining screws.
By the way, Simpson makes a wide range of galvanized steel connectors for framing elements. Although typically installed with special galvanized nails, Simpson has provision for use of screws as well. I don't really know how the IRC applies to use of screws with connectors, but as a professional engineer I spec screw connectors when I feel they are appropriate.