Will prior hospitalization for alcohol intoxication prevent the issuance of a first class medical cert.?
Possibly, but not necessarily.
First, nobody here is an AME, and a message board is the wrong format, if any of us were, to ascertain all the relevant facts.
Second, you'll need to put that hospitalization on the form you fill out for the exam. To omit it would be a criminal offense, so don't do that.
There are at least two things the AME will consider about what happened. First, is there any lasting damage from that incident? Second, does this indicate enough of an issue with alcohol that it has to go to OKC for their consideration? Both of those questions turn on the specific facts of your case. If both are &quot;no&quot; then your chance of losing the medical may be pretty low. Otherwise... it's all about how your case stacks up with the FAA rules and procedures.
Your best answer may be to consult with one AME to whom you are NOT applying for the medical, and get his expert opinion. Then, with that knowledge, apply (or don't) to your AME for the Class 1.
But please don't substitute internet forum opinions for professional medical advice from an actual doctor.