If the amount of people the Supply Corps has been picking up is any indication, I would say that currently, yes, they must be short, because they've been taking more people than any other designator. That's why I'm encouraging you to hop on the shuttle with us now, because if you're wanting to do it, now definitely seems like the opportune time.
When the current crop of OCs make it through their respective training periods, I am thinking the Supply Corps will be bulging with JOs, but who knows...gotta figure in attrition, transfers, retirement/separation, all that jazz. As many of the guys here will tell you, the needs of the Navy is a living, breathing organism, and is one of the few things in life that is genuinely constantly changing, sometimes right before one's very eyes.
As long as you've grabbed and have been using the study gouge on here, and are decent at basic applied mathematics, science, and logic (which is honestly what the reading portion is more like, not so much reading comprehension, more like "process of elimination" type reading, at least when I took it a year ago), you'll do fine. Let's put it this way: I hadn't even found this site yet, didn't know there was ANY study material for the ASTB (I didn't know about the ARCO guides and other stuff you could get at bookstores), and did pretty well. Had I gotten a leg up with the material here, I'd have done even better, I'm sure, if for no other reason than I would have known what to expect.
You'll do fine. Go in there and rock it, and come join the Chop Shop.