OK, I have managed to come up with a workaround for this:

Add a hidden column, also bound to CustomerID, to the grid.

Add a client event handler for the WebCombo's AfterSelectChanged event, which saves the data value to a global variable:

function CustomerIDCombo_AfterSelectChange(webComboId){
    var combo = igcmbo_getComboById(webComboId);
    newComboValue = combo.getValue();
}

Add a client event handler for the WebGrid's AfterCellUpdate event, which sets the value hidden column for the correct row to the value you saved from the combo:

function UltraWebGrid1_AfterCellUpdateHandler(gridName, cellId){
    var cell = igtbl_getCellById(cellId);
    if(newComboValue) {
        var row = cell.getRow()
        var hiddenCell = row.getCellFromKey("HiddenCustomerID");
        hiddenCell.setValue(newComboValue, false);
        newComboValue = null;
    }
}

And then you can reset the value of the real CustomerID field in the server-side UpdateRow event handler:

protected void UltraWebGrid1_UpdateRow(object sender, Infragistics.WebUI.UltraWebGrid.RowEventArgs e)
    {
        string customerID = e.Row.Cells.FromKey("HiddenCustomerID").Value.ToString();
        e.Row.Cells.FromKey("CustomerID").Value = customerID;
    }

Far from perfect, but it does appear to do the job.