Unfortunately I cannot repeat your situation and use ADODB. I recommend you to use native DAO library to work with MSJet (Access) database.
Sub qwe()
Dim dbe As New DAO.DBEngine
Dim dbs As DAO.Database
Dim rst As DAO.Recordset
Set dbs = dbe.OpenDatabase("C:\Users\nmaksudov\Documents\Database2.accdb")
dbs.Execute("UPDATE Table1 SET Field2='zzz' WHERE Field1=2")
Set rst = dbs.OpenRecordset("select * from Table1")
While Not rst.EOF
MsgBox rst.Fields(1).Value & "," & rst.Fields(2).Value
rst.MoveNext
Wend
MsgBox rst.RecordCount
End Sub
This should work perfect. Just add DAO library of correct version to your project. To find correct library open VBA editor in Access and choose Tools/References… menu. Find data access library in the list (in my case it is «Microsoft Office 12.0 Access database engine Object Library» or it could be «DAO 3.6» etc. Depens on version). After that open the same dialog in Excel and add the the object library.