It's possible to reserve a stack of that size, but only in Visual Studio. Besides, you're better off using the heap.
I suggest either implementing a linked-list, or allocating a pool of memory, and placing a resource inside the pool.
If you create a sf::Image on the stack only sizeof(sf::Image) bytes will be stored on the stack. The actual pixel data will be stored on the heap so it's probably not much to worry about.