You can forget the whole cursor type debate and just go with a modified SQL.
SELECT Count(*) AS RecordCount
FROM Table1;
This will return the number of records in the table.
ie:
Dim cn As ADODB.Connection
Dim rs As ADODB.Recordset
Dim lRecordCount As Long
Dim sSQL As String
Set cn = CreateObject("ADODB.Connection"

Set rs = CreateObject("ADODB.Recordset"
cn.Open "Microsoft.jet.OLEDB.4.0;data source ="path\dbname.mdb"
sSQL = "SELECT Count(*) AS RecordCount FROM TABLENAME"
rs.Open sSQL, cn, adOpenForwardOnly, adLockReadOnly, adCmdText And adExecuteNoRecords
lRecordCount = rs(0)