Yes, you could certainly be subject to a drug test while on probation. Standard rules and conditions of probation that I have seen in my practice include Alcohol & Drug Assessment to see if you have problems with substance abuse. Further, if your agent believes you are using drugs, he or she can ask you to submit to make sure you aren't breaking the law, which would be in violation of the standard rules of probation. He or she may or may not tell you ahead of time that you will have to do a drug test, and if you refuse a drug test it is seen as an admission that you are using drugs.
If you fail a drug test, your agent has several options. He or she may order you to undergo treatment for drug issues. He or she may sanction you to jail time as a punishment for your use. He or she may also revoke you from probation, sending you back to jail and potentially back before a judge to be sentenced for your battery charge.
Treatment before you get caught is better than hoping you only get treatment after you get caught. Running the risk of revocation is a big gamble, especially with an otherwise put-together life as you described.
I wish you the best of luck on probation.