Does ReverbNation distribute classical music?

Yes.  However, please note that classical releases must follow iTunes style guidelines which designate the formatting of the release.  Some key points to consider are:  

• Album title: Needs to include the composers, followed by a colon, followed by the work titles, catalog numbers, or type of works such as Sonatas or Preludes. For example:
•  Mozart: Requiem in D Minor, K. 626
• Track title: If a track features a movement or selection from a larger work like a symphony or concerto, begin the track title with the name of the larger work. This applies even if a track contains a portion of a movement, selection, or excerpt.  
• Primary Artists at the Track Level. All artists performing on a track must be marked as Primary. Do not enter Various Artists as an artist name at the track level. For example, if a track features:
• A violin sonata with piano accompaniment, mark both the violinist and the pianist as Primary
• For "classical-crossover", major work titles and catalog numbers must still be included, but may be presented at the end of the title within parentheses. For example, "Eine kleine Nachtmusik (First movement from Serenade in G Major, K. 525)"

Please see  Apple Music Style Guide 2.1.6 for further information.  

For standard composer names, album titles, song titles, catalog numbers, and other information for western classical music content, consult Baker’s Biographical Dictionary of Musicians, The New Grove Dictionary of Music and Musicians, or the International Music Score Library Project website.