Yes, Canvas will work perfectly with WooCommerce as long as your theme is optimized for mobile devices. Having optimized pages for the shopping cart, my account and payment sections is very important as they will not only improve the overall user experience but also increase the chances of having your app approved by Apple and Google.
Can I sell anything in my app?
You can sell physical products in your app, using your preferred payment method, like PayPal.Selling digital content is not allowed in the Apple App Store unless you used Apple's own in-app purchase system, which we do not support. So it might be a problem to sell downloads/content in the app.