Maybe. It depends on several factors. One is whether your PO ever finds out about it. You are supposed to inform your PO if you get arrested, and it is best to err on the side on caution and be up front with them about it. However, I've had some clients roll the dice and never get caught (when the new offense was a Class C like yours).
If no alcohol is a condition of probation, the PI is definitely grounds for violation. Some field officers will cut you some slack. And some judges have standing orders to be notified of any violation on DWI probation.
Unfortunately, there's no black-and-white answer on this.
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That would depend if you got processed through the jail and bonded out or they just held you in the drunk tank and gave you a ticket. If you were processes out through the jail chances are you PO will find out and you need to disclose your arrest. Either way hire a lawyer to take care of it. There is some old case law out there that your vehicle is not a public place.
As the others said, it depends. Look at the conditions of your probation. If they indicate that it is a violation to be Arrested then it may be considered a violation. If they say conviction is a violation, then simply being arrested is not a violation. Whether or not your probation will be revoked depends on many factors that are unknown from your question: how well you were doing on probation, the judge, prosecutor, county, local politics, etc. Texas Penal Code 49.02 explains public intoxication: Sec. 49.02. PUBLIC INTOXICATION. (a) A person commits an offense if the person appears in a public place while intoxicated to the degree that the person may endanger the person or another.
(a-1) For the purposes of this section, a premises licensed or permitted under the Alcoholic Beverage Code is a public place.
(b) It is a defense to prosecution under this section that the alcohol or other substance was administered for therapeutic purposes and as a part of the person's professional medical treatment by a licensed physician.
(c) Except as provided by Subsection (e), an offense under this section is a Class C misdemeanor.
(d) An offense under this section is not a lesser included offense under Section 49.04.
(e) An offense under this section committed by a person younger than 21 years of age is punishable in the same manner as if the minor committed an offense to which Section 106.071, Alcoholic Beverage Code, applies.
A lawyer may be able to help you challenge the public intoxication charge which may help minimize your chances of having your probation revoked. Good luck.