Yes, in C/C++ you can access memory outside of the space you claim to have allocated. Sometimes. This is what is referred to as undefined behavior.
Basically, you have told the compiler and the memory management system that you want space to store four integers, and the memory management system allocated space for you to store four integers. It gave you a pointer to that space. In the memory manager's internal accounting, those bytes of ram are now occupied, until you call delete[] arrayPtr;.
However, the memory manager has not allocated that next byte for you. You don't have any way of knowing, in general, what that next byte is, or who it belongs to.
In a simple example program like your example, which just allocates a few bytes, and doesn't allocate anything else, chances are, that next byte belongs to your program, and isn't occupied. If that array is the only dynamically allocated memory in your program, then it's probably, maybe safe to run over the end.
But in a more complex program, with multiple dynamic memory allocations and deallocations, especially near the edges of memory pages, you really have no good way of knowing what any bytes outside of the memory you asked for contain. So when you write to bytes outside of the memory you asked for in new you could be writing to basically anything.
This is where undefined behavior comes in. Because you don't know what's in that space you wrote to, you don't know what will happen as a result. Here's some examples of things that could happen:
The memory was not allocated when you wrote to it. In that case, the data is fine, and nothing bad seems to happen. However, if a later memory allocation uses that space, anything you tried to put there will be lost.
The memory was allocated when you wrote to it. In that case, congratulations, you just overwrote some random bytes from some other data structure somewhere else in your program. Imagine replacing a variable somewhere in one of your objects with random data, and consider what that would mean for your program. Maybe a list somewhere else now has the wrong count. Maybe a string now has some random values for the first few characters, or is now empty because you replaced those characters with zeroes.
The array was allocated at the edge of a page, so the next bytes don't belong to your program. The address is outside your program's allocation. In this case, the OS detects you accessing random memory that isn't yours, and terminates your program immediately with SIGSEGV.
Basically, undefined behavior means that you are doing something illegal, but because C/C++ is designed to be fast, the language designers don't include an explicit check to make sure you don't break the rules, like other languages (e.g. Java, C#). They just list the behavior of breaking the rules as undefined, and then the people who make the compilers can have the output be simpler, faster code, since no array bounds checks are made, and if you break the rules, it's your own problem.
So yes, this sometimes works, but don't ever rely on it.