The short answer is: no. C++ does not employ garbage collection, like Java or C#. When an object is destroyed, it's destroyed immediately. Gone for good. Joined the choir invisible. Pining for the fjords, etc...
And to say this over a couple of times in different words so that there is no possible weasily reinterpretation...
The destructor is invoked as part of object destruction. Object destruction consists of invoking the destructor and deallocating the memory that was used for the object itself. It's a single process, not two separate processes. While the destructor is running, the object still exists, for the destructor to use, but it exists on borrowed time. It's a foregone conclusion that the object is going to be vaporized as soon as the destructor returns. Once a destructor is invoked, the object is going to be destroyed, and nothing is going to change its fate.
Understand this: the reason why a destructor is being invoked is because either: the object was originally allocated on the heap with "new", and it's now being "delete"d. "delete" means "delete", not "delete maybe". So the object's getting deleted. Or, if the object was allocated on the stack, the execution thread exited the scope, so all objects declared in the scope are getting destroyed. The destructor is, technically, getting invoked as a result of the object being destroyed. So, the object is being destroyed. The End.
Having said that, C++ allows you to implement a custom allocator for your classes. If you feel like it, you can write your own custom memory allocation and deallocation functions that implement whatever functionality you want. Though these are never used for stack allocated objects (i.e. local variables).