No. Static class variables behave as they should, with it’s value shared only within the instance it is instantiated in. Thus, static variables should not be used to synchronise or provide locks between role instances.
To confirm this behaviour, I created a simple web role with a button that sets a static class variable. A timer periodically triggers to attempt to retrieve the variable to displays it. The web role then deployed with at least 2 or more instances.
From the screen below, we can see that each web role instance read a different GUID value from the GUID static class variable.
However, access to the same web role instance read back the same GUID value.
Hit the link below for the source files if you want to test it out.
Hope this is remotely useful for some other Azure beginner like me .