Active Fault Codes
An active fault code is at) indication of a fault that is currently triggered.
The active fault may or may not compromise normal operation of the related system(s). Service action in B.U.D.S. should be used to correct the problem that caused the fault code.
Once the fault condition(s) of the active fault is no longer present, its state will change to "occurred".
Occurred Fault Codes
An occurred fault code indicates a fault that was active, but no longer is.
The occurred fault does not presently affect system or component operation but is retained as a history of the faults that were detected.
Inactive Fault Codes
An inactive fault code represents a fault code that is neither active, nor occurred. It is simply part of a list of all possible faults which may be monitored by the various ECUs, which may become active or occurred if the monitoring system detects an applicable fault.
The answer is yes to your question, BUDS system will read and display all three types of faults.