Melkor was probably at the height of his powers as the Dark Lord of Utumno, in the years before the coming of the Elves and even before the founding of Valinor. At that time he was able to make an assault on the Valar, and destroy the Lamps, but even so he was still driven back and had to go into hiding in Utumno.
The Silmarillion notes:
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And the Valar could not at that time overcome him, for the greater part of their strength was needed to restrain the tumults of the Earth, and to save from ruin all that could be saved of their labour; and afterwards they feared to rend the Earth again, until they knew where the Children of Ilúvatar were dwelling, who were yet to come in a time that was hidden from the Valar.
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So it seems clear that even then the Valar could have overpowered him, if they hadn't been distracted by other concerns. Subsequently there were only two main conflicts, the Sack of Utumno and the Captivity, and the War of Wrath, in both of which the Valar were victorious (it's actually doubtful if the Valar even took part in the War of Wrath).
So no, it doesn't seem likely that Melkor/Morgoth would have been able to undertake a successful attack on Valinor at all.