No, You would need to instantiate a new ActiveX exe for each download inside the loop. Something like this
Code:
Dim ActX() as DownloaderActX.download

Redim Actx(Me.MSHFlexGrid1.rows - 1)

For i = 1 To Me.MSHFlexGrid1.rows - 1       'All filenames in WWW are in the MSHFlexGrid
    Set ActX(i) = New DownloaderActX.download
    ActX(i) Me.MSHFlexGrid1.TextMatrix(i, 1)   'send the filename to 
Next i
This would start as many downloads as you had rows. I would not recommend running that many though it is just an example.