Will adding product categories to the featured products on my home page increase conversion?
(the name of the category under the left title is also a link to that category)
Not only that, it's encouraged to do so. the main reason is to increase "findability". If buyers (users) can't find the product they're after - it won't get sold. Because of that, there is a long checklist to follow when adding categories to an e-commerce site, all of it, by Christian Holst. All of the bullets isn't category related, but it shows the necessity of navigation:
Categories is not only a good idea, it's the one thing you need to address when addressing navigation issues on an e-commerce product page. It could be extended by using faceted navigation as a complement to the web site category based navigation.
Reference: Categories, Facets—and Browsable Facets?
In SharePoint out of the box, the product category navigation is implemented by default. The only thing needed to be done, is to map each product with the correct category in the term store. But it's there for the same reason - making users find their products.
Reference: Stage 3: How to enable a list as a catalog
An A/B test experiment can help determine the answer since it can go either way depending on the type of users on your site and the type of 'conversion' you're referring to (purchased, view product detail, sign up for account..etc).
My assumption is that adding the product category will encourage the users to click on category and view more related products, therefore users will be less likely to click on/purchase the item displayed on the home page but may ended up purchasing a different product due to more options for comparison. This is just a guess, so I highly recommend running a test to find out.
According to this Baymard Institute article it should help as it is promoting what the store actually sells.
Each category gives the visitor a grasp of what they can expect, while also reducing wasteful clicks (as some users click on the product only to then click on the product category in the breadcrumb).
Any answer would be a generalisation to help you with a 'best guess'. As everyone has said. You need to A/B test.
However, it's worth bearing in mind that users - when presented with too many options, often don't choose any of them.
The rationale of a limited amount of clicks is a fallacy. Just because you're 'forcing' users to make one more click before they get to the buy buttons doesn't mean that there imaginary click quota is suddenly empty.
By filtering you are giving users clear areas that are easier to visually digest and compare. Progressive disclosure helps users to get to where they want, opposed to throwing everything at them on the home page in case they miss something that's hidden behind a click.
Make your categories clear and concise, they'd need to easily describe what's contained within. This may be where you become unstuck in an A/B scenario.
Finally, consider adding a search and make it high visual priority. This will allow those who know what they want to get to it quickly. And comfort those who are intimidated by product categorisation and filtering.
Source: Iyengar, Sheena S. and Mark R. Lepper. 2000. When choice is demotivating: Can one desire too much of a good thing?. Journal of Personality and Social Psychology. 79: 995-1006.