Basically no. Elements in the vector are default constructed upon a resize (for an integer this results in 0).
Assuming you are using reserve() to ensure that resize() does not allocate memory I would not worry about this unless it proves to be a performance issue later on.
If you are concerned you may wish to consider just using a regular array and storing the item count in a separate variable. This will give you the best performance.
Update:
John asked:
Is the constructor really guaranteed
to zero that memory? I thought that
was undefined?
Yes and no. The primitive types (int, bool, float, etc) do have default constructors that initialize them to zero. However unlike regular classes or structs the compiler does not automatically call them.
E.g
int a; // uninitialized
int b = int(); // initialized to 0
Because vector::resize uses the latter form when adding items you are guaranteed that the elements created will be correctly initialized to zero. This is true of all the STL collections that implicitly create elements.