Yes, you should test your packaging, but the way you test depends entirely on where your customers buy from you. The goal of packaging for an Amazon-first brand is very different from that of a direct-to-consumer brand, and your testing method needs to reflect that.
For a brand selling on a marketplace like Amazon, the packaging is part of the digital shelf. It's often a key element in your product photography. As Anthony Cofrancesco detailed on Actualize Freedom, testing this can directly improve your conversion rate, because shoppers see it before they even click "add to cart." On the Serious Sellers Podcast, the hosts often discuss how running polls or even live A/B tests on your listing can de-risk a launch on Amazon. Committing to a massive, expensive print run without this data is a huge gamble, and testing helps you avoid a design that completely flops.
For a DTC brand, the context is completely different. The customer has already purchased the product. As Jason Wong explained on the Up Arrow Podcast, the package that arrives at their home is not a conversion tool, it’s a marketing channel inside their house. Here, the goal is the unboxing experience and post-purchase brand reinforcement. You aren't testing for click-through rate, you're optimizing for brand perception and storytelling. A/B testing for sales lift is less relevant than gathering qualitative feedback to see if the design strengthens your brand and makes customers feel good about their purchase.