Have I understood what Arduino is correctly?
No, you misunderstood. The chip isn't blank (also you don't insert the chip into Arduino. It comes with the Arduino). It has a special bootloader which is actually the core of the Arduino platform and which allows Arduino not to have a special programmer to program the chips. So it will not work with blank chips at all. Furthermore you're limited only to chips which are supported by the bootloader or are very similar.

Also from what I can see, the Arduino IDE doesn't have a simulator, so you're out of luck on that point.

The main point of Arduino is that it hides the physical operation of the chip itself from the programmer making it easier to use for those that find it too complicated to start programming the chip directly. It offers a simplified C-like programming language and it has a large library of functions which make it easy to connect various peripherals. The PCB itself is useful since it allows users to have a good quality base from which to make their own devices and saves them the trouble of making a PCB which will drive the AVR themselves or using some type of prototyping board.

Basically what you want is regular Atmel's IDE called AVR Studio which does have a simulator (you can download it freely and check if it suit your needs). On the hardware side, you'll need either a programmer, if the IDE's simulator is fine, or a in-circuit emulator which will allow you to directly debug the code on the chip. The emulator itself is pretty expensive, but there are some other products that will allow you to step through the code too.

Do note that it is possible to make an AVR programmer using Arduino but that isn't a major advantage over other programmers available on the Internet or the official programmer.