Will ternary computers be faster than binary?
It depends. A number represented in base 3 will have fewer digits than the same number in base 2. Perhaps this means computations will be faster, since you have to work with fewer digits. However, perhaps the operations will become slower (since they're more complicated) so there might be no net gain - or perhaps even worse performance! There's no way to tell how fewer, complicated operations will compare to more, but simpler operations.

Another consideration is arithmetic. If you are working in base 10, then division by 10 is really easy with divisions in other bases being more work. Similarly, in base 2, division by 2 is easy. In base 3, division by 3 would be easy. If your application requires frequent division by 3, then base 3 would be beneficial.