No. Unless you've bought an Anytime or BS ticket, it simply means that you are first in line to be able to pay more to fly standby. (Or, in IROPS, or because of a delay, not pay more but jump to the front of the standby line.)
EDIT: From the
FAQ, it appears that maybe Priority Standby does
not help in IROPS:
How does priority standby work for A-List and A-List Preferred Members?
When requesting standby travel, A-List and A-List Preferred Members will automatically be placed at the top of the standby traveler list. All qualifying A-List and A-List Preferred Members benefit from priority standby, with A-List Preferred Members placed at the top of the list, followed by A-List Members. Priority standby will only be provided for A-List and A-List Preferred Members. If an A-List or A-List Preferred Member is traveling on a multiple-passenger reservation, priority standby will not be provided for non-A-List or non-A-List Preferred Members in the same reservation. For A-List and A-List Preferred Members who are also Companion Pass Holders, priority standby will not be provided for the Members' designated Companion unless he or she is an A-List or A-List Preferred Member. Irregular operations may affect the Priority Standby benefit.