Carjul,
Technically you could do that. But you would have to put a 20 ft tall trellis up, for the vines to climb on.
How would you maintain the vines on a 20 foot trellis?
What about fast growing trees that aren't real invasive?
I don't know what zone you are in, you could look online and see if there are some that will grow well in your area.
If you put decidieous trees there, you would have privacy in the months that you will be outside the most, and they grow faster (generally) than evergreens.
That is what I would look into.
Some nurseries will sell bigger trees also, ask.