Yes, AR 601-280 chapter 8 covers Bars to Reenlistment. With regard to appeals it states:
Soldiers desiring to submit an appeal who are otherwise qualified under the criteria of chapter 3, including those with approved waivers, will not be involuntarily separated while an appeal is pending. Should the soldier desire to submit an appeal, but refuses retention to allow processing of the appeal, he will be informed that the bar will remain in effect. From the time he is informed that the bar was approved, the soldier will be allowed 7 days to submit an appeal. On a case-by-case basis, an extension of this period may be granted by the commander initiating the bar procedure. Appeals will be endorsed personally by each commander (or acting commander) in the chain of command, and approved or disapproved by the proper authorities shown in (1) or (2) below. Final approval of appeals will be at least one approval level higher than the original bar approval authority.