No, Maa Saraswati did not play a role in convincing Manthara as per Mahabharata. Manthara happened to be an incarnation of Gandharva by the name of Dundubhi, who followed directions from Lord Brahma

From Mahabharata's Vana Parva

And at this, the gods, the Gandharvas and the Danavas quickly assembled to take counsel as to how they should be born on earth according to their respective parts. And in their presence the boon-giving god commanded a Gandharvi, by name Dundubhi saying, 'Go there for accomplishing this object!' And Dundubhi hearing these words of the Grandsire was born in the world of men as the hunchbacked Manthara

And then

And the adorable Creator of the Universe, having ordained all this, instructed Manthara as to what she would have to do. And Manthara quick as thought, understood all his words, and went hither and thither ever engaged in fomenting quarrels.

So as seen here she was following directions from Lord Brahma.

As per Mahabharata. Manthara happened to be an incarnation of Gandharva by the name of Dundubhi, who followed directions from Lord Brahma

From Mahabharata's Vana Parva

And at this, the gods, the Gandharvas and the Danavas quickly assembled to take counsel as to how they should be born on earth according to their respective parts. And in their presence the boon-giving god commanded a Gandharvi, by name Dundubhi saying, 'Go there for accomplishing this object!' And Dundubhi hearing these words of the Grandsire was born in the world of men as the hunchbacked Manthara

And then

And the adorable Creator of the Universe, having ordained all this, instructed Manthara as to what she would have to do. And Manthara quick as thought, understood all his words, and went hither and thither ever engaged in fomenting quarrels.

So as seen here she was following directions from Lord Brahma.