I started buying Tiffany silver ~1-2 years ago. I've left them in the pouches but also in a small ziplok bag too to minimise air contact.
I'm not sure to the exact answer to your question as I haven't experienced it. However if I were to guess I would say they would be more prone to tarnishing in your jewellery box unless your jewellery box was tarnish treated (wolf is a brand that comes to mind).
There are other members who are more experienced in this regard though.
I can suggest this thread which I recall had some good information:
There a simple and not terribly pricey solution, a Wolf Jewelry Box. There are many styles and sizes, all with one thing in common -- an interior lining to keep your silver jewelry tarnish-free for several decades. Here's a link to what's available at Neiman Marcus, although there are many other places to purchase Wolf jewelry boxes: Click Here