The title is self explanatory - does the standard vector implementation take care of deallocating dynamic memory pointed to by all the pointers that are in the vector?
No. When you destroy a std::vector it destroys all its elements (calls their destructor) and then deallocates the storage used by the objects. But a (raw) pointer does not have a destructor - destroying it does not deallocate the object it points to - it just destroys the storage used to hold the pointer itself.
If you had had a vector of smart pointers (std::unique_ptr or std::shared_ptr) then it would be a different matter. Those classes do have destructors and do deallocate what they point to upon destruction (unique_ptr always, shared_ptr if it's the last object pointing to the contained object, otherwise it just decrements its reference count).
Note: a std::unique_ptr is a very thin wrapper around a raw pointer, that is designed to optimize away completely. So, using it should have zero overhead over a raw pointer when optimization is enabled. So it'll give you the semantics you want with no overhead compared to doing the manual memory management - manually.