try calling a recruitment station and ask about it
In general...No, unless you conceal the diagnosis. Eventually it will be found out and you will be charged under the Uniform Code of military justice and dishonorably discharged.
There is a caveat. If there was a single incident in your life (a car crash in which a family member perished), you may be upset and treated briefly, and end up with a PTSD diagnosis in your record. In this case you will have to go before a medical board for a waiver.
A DD requires a court martial, and lying on enlistment, isnt a cause for such a serious punishment. But, being labeled with fraudelent enlistment can. i actually looked into joining near the end of 2012, before i transfered to a 4 year school. I found out so many things can get you disqualified. PTSD is PDQ, and depending on circumstances it may require waiver, but in most cases because of treatment,medicaiton it can dq you. Just be aware of that. The current military drawdown also restricts and tightens enlistment standards.