Can I use a 17th Avenue theme with the WordPress.com Business Plan?

Yes, you can!

However, we always recommend self-hosted WordPress.org as the best option. With self-hosted WordPress.org, your site is yours alone and you can do whatever you want with it.

Self-hosted WordPress.org is also considerably less expensive than the WordPress.com Business Plan. Shared hosting from Bluehost or SiteGround is as low as $4/month, versus $25/month for the Business Plan.