Silver tarnish is silver sulfide. It is conductive, but not as conductive as silver oxide. Normally, silver oxide is the concern when silver is used in electronic applications, though it's probably not such a problem for audio.
The silver in these type of materials serves to drastically lower the contact resistance at the point of connection. The effect of this is to lessen the bottleneck effect, probably by at least 3 orders of magnitude at the very minimum, electrons face at a point of connection. I believe this is most probably the reason we hear such sonic differences with these materials, as opposed to oxidation, because silver itself is not immune to oxidation.
Silver, as opposed to the seven other precious metals, is the one to worry about when it comes migration. However, it is mostly related to soda lime glass. The soda (sodium oxide) is used to lower the melting temperature of the glass, and improves the surface quality of the quenched (solidified) glass. Silver will migrate through this type of glass when an electrical current is passed through it, due to the presence of the sodium. The way to prevent this is to alloy the silver with at least one other precious metal (normally palladium or platinum), or use a different type of glass. I would think almost none of us are using the SST/ESST on glass, let alone soda lime glass, so, like the silver oxide issue, the point is probably moot.
The ONLY worry I have with these materials is that one must be extremely careful to not build up enough material (either in one large application, or cumulative applications over time) to short something out, and cause a component to fail catastrophically. Be EXTRAORDINARILY vigilant in this area - to the point of visually inspecting this after applying the material even if you have to take your gear apart to do so (if used on tube pins, tube sockets, etc.).