What is dead arm? Serious question.
Another serious question - why not just give him an MRI? Is there any harm in doing it? I've gotten an MRI on my knee and they didn't inject anything - I was pretty much in and out. Would a shoulder MRI be of the type comish4life described and require time off from pitching? They spent lots of money signing him so spending a few extra bucks to protect the investment would make sense so the cheap argument doesn't really hold much water in my book.
A dead arm is just that, a dead arm.
For a major leaguer who normally throws 94, with a dead arm will throw 80. He'll be maxing out, throwing with little to no discomfort, but with no results.
As for an MRI with dye, it depends on the patient's symptoms and history. It's usually not the first course of action, however, it was indicated in my situation. I've since had my biceps relocated to address the tear in my labrum.