In the homepage categories section

These links help users decide which path they should take to find the product they want

It also helps returning users bypass intermediate pages and go directly to the sub-sub-category they want.

 

Not common

I looked at 55 of the top ecom stores, and haven’t found a single one that is doing this. However, most of them have at least a thumbnail to illustrate the category, and several of them also added a label.

 

An alternative

Instead of putting 2 or 3 levels of navigation links in the categories section of the homepage, you can instead have a section with the main categories, followed by a section which allows users to browse through sub-categories.

 

Sub-sub category links

If you have a section to browse sub-categories, you could possibly put sub-sub category links under the sub-categories.