Move an Object Smoothly through an Array of Vertices?

Is it possible to move an object in unity through an array of Vector3[] vertices?

And if I can do that can I make it so that it goes fast in the beginning but it slows down a tad bit for a realistic look?

I don't see why that would be a problem. Take a look at iTween, it's a free animation library that you could use to get the exact effect you're looking for.

It's also available in Javascript or C# so you're set unless you really like Boo (but as far as I know all the languages are inter-operable in unity to some degree).

Hope that helps and good luck!