Well, I wouldn't call it exactly "a simulator", but yes, Win64 is able to execute 32bit user-mode applications without any problems.
What it can't do, however, is to load 32bit drives - only 64bit drivers are supported. So, your application can be 32bit, but if it requires special drivers to work correctly, updated 64bit ones have to be supplied (which affects low level programs like antiviruses, and their resident protection in particular, probably CD burning tools, etc.)
And no, Win64 does not have a 16bit virtual environment - Win16 or DOS executables are not supported anymore there and can't be run.