No, there will not be any collisions between application global variables as long as the two application directories are truly separate and don't include files from one another. When a PHP script runs, the HTTP request that initiated it can be thought of as an isolated incident. It is separated and isolated from all other requests to the same application (even concurrently) and from other applications.
Each script gets its own variable namespace when execution starts, and that environment is terminated and deleted from memory when the script completes.
Now, if you happen to be using $_SESSION and both applications use the same value for session_name() and run on the same domain name, there is the possibility that values persisting in $_SESSION can collide between your application instances. This is simply solved by changing the value for one of the applications from the default PHPSESSID:
// Application 1
session_name("APP1");
session_start();
// Application 2
session_name("APP2");
session_start();
You probably are already aware of this, but I'll say it to be complete. Wherever possible, it is advised to abstract out aspects of the code that can be shared between the two application instances and included by both of them. This is in keeping with the DRY principle, and will save you lots of headaches if you ever have to make modifications to the code both applications share.