Sharepoint - Query SP2013 Managed metadata term store
I've recently written a post on how to access Term Store in SharePoint 2013 using the javascript "SP.Taxonomy.js"
Hope it helps you. http://cann0nf0dder.wordpress.com/2013/04/09/accessing-taxonomy-term-store-with-jsom/
JSOM or REST API = no. BUT you can use JavaScript to call the Taxonomy Web Service to effectively accomplish client-side access. It's definitely more cumbersome than using the CSOM or REST API, though, but it works.
Try this out: http://spandps.com/tag/web-services/
The taxonomy picker with suggestions uses this web service client-side.
UPDATE: See the other answers. Sorry for the misinformation re: JSOM; I was thinking SharePoint 2010.