Insofar as I can tell, Viola’s master plan is deeply flawed. She hears about Orsino, and about how Olivia is spurning the advances of men. She then wishes that she could serve at Olivia’s side. The Captain informs her that Olivia will see no one anymore, especially messengers from the Duke. Hearing this, she decides to disguise herself as a boy and become the Duke’s servant, so that she can… um… well, I’m not entirely sure.
I mean, I know why she disguises herself: she says she wants to hide her identity for a while to recover from recent tragedy. That’s just peachy. But why is she serving the Duke? The Captain just said that the Duke’s servants are getting turned away from Olivia’s door, so why would Viola bother? Honestly, she’d probably have better luck serving Olivia if she just went to see the lady herself, cutting out the Duke entirely. But whatever. Stupid plan or not, the Captain swears to help Viola strap down her lady parts and get a job with Orsino. Huzzah. Her biggest selling point to the Duke? She can sing! Apparently, Orsino’s standards in servitude are pretty low.