AD is correct.
If the soldier is eligble for automatic promotion to E4, the only way to stop the promotion is the Co Cdr must submit a DA 4187 flagging the soldiers
DA 600-8-19, Chapt 2-3d, "If a unit CDR elects not to recommend a Soldier for promotion on the automatic promotion date, then a DA Form 4187 denying the promotion will be submitted not later than the 20th day of the month preceeding the month of automatic promotion."
With an automatic promotion, the Commander does not recommend promotion. A list of eligble soldiers is given to the CDR, the promotions will go through unless the CDR actively submits a DA 4187 to flag the soldier.
AR 600-8-19 Chapt 2-3e, "The DA Form 4187 denying the promotion (in lieu of DA Form 268) will be used by the BN HR to initiate a FLAG transaction using code PA as the initial and reason code and input the transaction into the automated system. This will stop an automatic promotion. The FLAG must be closed using FLAG code PE not later than the second working day following the date the Soldier would have been automatically promoted."
Unfortunately, since going to the SotM board is suppose to be voluntary, It would be very difficult to deny the promotion on that basis.
If your First Sergeant does this, I strongly suggest that you and the soldier make an appointment to see the JAG Attorney assigned to your Brigade. He/She will most likely work out the SJA office at Division HQ in the Crim Law Section. He may not be able to help but he should be able to direct you to to who can. If all else fails, go to the IG's office.