First, I'd wait to see if that date really stays unchanged -- from the various trackers (e.g.
http://www.immigrationportal.com/showthread.php?p=947118#post947118) we know there are many cases well before 06/01/03 which haven't been processed yet. The VSC has posted "optimistic" dates in the past then reverted them a couple hours / days later.
Second, I believe you can't initiate an inquiry until they are 60 days past your case ND. So if your ND is 06/01/04, they'll need to hit 08/01/04 first Assuming they don't change the published processing date I wouldn't be surprised if they start to force people to wait 120 days or longer before accepting inquiry requests.
Personally, even if I had an ND of 04/01/04 and could theoretically initiate an inquiry, it's probably not worth it -- I'd give them at least a couple more months based on the tracker and on the stats at sites like rupnet.com.
Questions:
Does anyone know for sure whether they go off the RD or ND for processing cases -- I thought it was the ND but someone suggested earlier today that it's the RD (and the PD for labor substitution cases).
Also, haven't some people been told they can't initiate an inquiry until the number of days on the notice has passed?
ETA