If the correction under an IRS correction program is for the plan sponsor to make a QNEC contribution (for example, a failed ADP tested not corrected by the end of the following plan year), but the plan document does not provide for QNEC contributions, must the plan document be amended before the correcting QNEC contributions can be made?

Yes. The plan document needs to be amended. So saith the IRS in Rev. Proc. 2001-17 at page 595, "[I]f a Plan Sponsor corrects an Operational Failure in accordance with SCP or VCO, it may amend the plan to the extent necessary to reflect the corrective action. For example, if the plan failed to satisfy the [ADP] test . . . and the Plan sponsor must make qualified nonelective contributions not already provided for under the plan, the plan may be amended to provide for qualified nonelective contributions."