Max train car height - Model Railroader Magazine

20'-2" is also the max height for double stack container cars.

BUT, the answer to your question is: "It all depends." 

Some routes have very tight vertical clearances.  Those routes might not allow the above cars to clear.

There are certain standard clearances for freight cars (both with and without loads).  They are called plates.  There is B (the tightest, with a vertical clearance of 15'-1"), C, E, F, and H.  H is 20'-2".

Widths are also mentioned in the specifications.  You didn't ask about those, though.

To further investigate "plates", get a copy of "The Official Railway Equipment Register".  They come out quarterly.  Various editions can be found used on Ebay.  Look through the back of the book, and you'll find the plate drawings.

Ed