Do local var assignments in batch files have priority over global env vars even for programs ?

Assume the system PATH variable is set in Control Panel->System globally as:

PATH=D:\aaa\bin;D:\bbb\bin

Then I start a DOS batch file mytest.bat with the following content:

set PATH=D:\bbb\bin;%PATH%

Note that the folder D:\bbb\bin has now priority over D:\aaa\bin!

Now I start from within the same batch file a program:

myprog.exe param1 param2

Does this program now use (if necessary) programs from the aaa\bin or bbb\bin
directory?

If the programs uses the globally defined vars and ignores the just done assignments:
Is there a way to create a local, temporarily changed environment for the run of a certain program otherwise?

Michael