The following exception is thrown during the start-up on windows (Sun JDK).
The system property is in fact set as the error message suggests and I can successfully invoke

java.util.logging.Logger logger = java.util.logging.Logger.getLogger("mylogger");
System.out.println(logger.getClass().getName() + " " + logger.getClass().getClassLoader().getClass().getName() + " " + logger.getClass().getClassLoader());

from ManagedProcess just before

this.log = Logger.getLogger("org.jboss.process." + processName);

(which causes the error) and output will be

org.jboss.logmanager.Logger org.jboss.modules.ModuleClassLoader ClassLoader for Module "module:org.jboss.logmanager:jboss-logmanager"

Exception in thread "main" java.lang.IllegalStateException: The LogManager was not properly installed (you must set the "java.util.logging.manager" system property to "org.jboss.logmanager.LogManager")
at org.jboss.logmanager.Logger.getLogger(Logger.java:60)
at org.jboss.logging.JBossLogManagerProvider.doGetLogger(JBossLogManagerProvider.java:55)
at org.jboss.logging.JBossLogManagerProvider.getLogger(JBossLogManagerProvider.java:46)
at org.jboss.logging.Logger.getLogger(Logger.java:2222)
at org.jboss.as.process.ManagedProcess.<init>(ManagedProcess.java:66)
at org.jboss.as.process.ProcessManagerMaster.addProcess(ProcessManagerMaster.java:64)
at org.jboss.as.process.ProcessManagerMaster.main(ProcessManagerMaster.java:52)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at org.jboss.modules.Module.run(Module.java:105)
at org.jboss.modules.Main.main(Main.java:169)