Can I add wholesale tiers while I am editing a product, without leaving it?

Yes. When the plugin is active, each product's edit screen has a Wholesale tab in its tab bar.

1. Open the product and click Wholesale.
2. The tiers page opens for that product only, so there is no product to pick.
3. Click + Add tier, enter Min quantity and Unit price, and click Save tiers.
4. Click Back to product to return.

You can still manage every product from Products → Wholesale Pricing, where Products with wholesale tiers lists all of them with an Edit link.