msboxシートに全員の名前とチェック済み有無の数式を書いて置けば、
マクロではシートを表示させ、オートフィルターするだけで良いと思います。

その一例です

Const SHNAME = "アルコールチェック"
Const msbox = "msbox"

Sub test()
    If Not Evaluate("isref(" & SHNAME & "!a1)") Then dataset    'この行不要
    With Worksheets(msbox)
        .Activate
        .Unprotect
        .Range("A:B").AutoFilter 2, "0"
        .Protect AllowFiltering:=True, UserInterfaceOnly:=True  '他の人に弄られないようにするため
    End With
End Sub

'以下は不要
Private Sub dataset()
    Dim sh As Worksheet
    Dim n As Long, i As Long
    Dim rng As Range
    
    n = 15
    Set sh = Worksheets.Add
    With sh
        .Name = msbox
        .Range("A1") = "名前"
        For i = 2 To n + 1
            .Cells(i, 1).Value = Chr(i - 2 + Asc("A")) & "さん"
        Next
    End With
    With Worksheets.Add
        .Name = SHNAME
        For i = 1 To Day(Date)
            Set rng = .Cells(.Rows.Count, "C").End(xlUp).Offset(1)
            rng.Resize(n) = "=rand()"
            sh.Range("a2").Resize(n).Copy rng.Offset(, -2)
            rng.Offset(-1, -2).Resize(n + 1, 3).Sort rng, xlAscending, Header:=xlYes
            rng.Resize(n).Value = Month(Date) & "/" & i
            rng.Offset(WorksheetFunction.RandBetween(n - 5, n), -2).Resize(n, 3).ClearContents
        Next
        rng.Offset(WorksheetFunction.RandBetween(n - 10, n - 5), -2).Resize(n, 3).ClearContents
    End With
    With sh
        .Range("B1").Formula = "=today()"
        .Range("B2").Resize(n).Formula = "=COUNTIFS(" & SHNAME & "!A:A,msbox!A2," & SHNAME & "!C:C,msbox!B$1)"
'        .Range("A1").CurrentRegion.AutoFilter 2, "0"
        .Protect AllowFiltering:=True, UserInterfaceOnly:=True
    End With
End Sub