It's actually possible to do this with 1st generation Camaros (1967-69). Someone thought ahead and saved the original tool and die casts before GM destroyed them. Some googling will find you sources for parts: from frame and body to seats adn trim. From what I've read, it costs somewhere in the realm of 12-20k. Not bad for a clone of what is the most fantastic American muscle car to ever be made with modern reliability.
There's a company (http://www.ultimasports.co.uk/canam/index.html) that sells kit super-cars. According to them it takes 40 - 80 hours to put together what is essentially a car that is 95% as good as some Italian machine but at 10% of the cost. Not bad considering what you are getting.
Assembling a batch of nice fresh parts is a lot easier than you think. Unless you have to assemble/rebuild the whole engine by hand, you will probably spend more time waiting for the paint to dry than you will putting it all together.
Not necessarily; ever put together one of those Saga electric guitar kits? I've spent maybe 5-10% (out of maybe 15-20 total build time) tweaking and adjusting, finding they didn't drill all the holes in the right places, etc.