I am considering using virtual inheritance in a real-time application. Does using virtual inheritance have a performance impact similar to that of calling a virtual function? The objects in question would only be created at start up but I'm concerned if all functions from the hierarchy would be dispatched via a vtable or if only those from the virtual base class would be.
Common implementations will make access to data members of virtual base classes use an additional indirection.
As James points out in his comments, calling a member function of a base class in a multiple inheritance scenario will need adjustment of the this pointer, and if that base class is virtual, then the offset of the base class sub-object in the derived class's object depends on the dynamic type of the derived class and will need to be calculated at runtime.
Whether this has any visible performance impact on real-world applications depends on many things:
Do virtual bases have data members at all? Often, it's abstract base classes that need to be derived from virtually, and abstract bases that have any data members are often a code smell anyway.
Assuming you have virtual bases with data members, are those accessed in a critical path? If a user clicking on some button in a GUI results in a few dozen additional indirections, nobody will notice.
What would be the alternative if virtual bases are avoided? Not only might the design be inferior, it is also likely that the alternative design has a performance impact, too. It has to achieve the same goal, after all, and TANSTAAFL. Then you traded one performance loss for another plus an inferior design.
Additional note: Have a look at Stan Lippmann's Inside the C++ Object Model, which answers such questions quite thoroughly.