No purchasing a domain name and domain mapping does not change any of the rules at all.
Before Upgrading – Important Notes
Same Rules Apply – The Domain Mapping Upgrade does not enable the permission to use advertising, any kind of prohibited code, or upload additional themes or plugins. With the upgrade, your blog will still be hosted here at WordPress.com, which means that you will not have FTP access to your files and you will still be required to abide by our Terms of Service. http://en.support.wordpress.com/domain-mapping/#before-upgrading-important-notes
In a nutshell free blogs from and being free hosted by wordpress.COM cannot be used to drive traffic to third-party sites by means of advertising and/or affiliate programs (see next section for more clarity). E-commerce transactions via shopping carts and the like cannot be conducted on wordpress.COM blogs. No retailing or reselling the work created or services provided by anyone other than yourself is allowed.
Affiliate marketing blogs
The only exceptions with regard to affiliate links are found here:
Affiliate marketing blogs: Blogs with the primary purpose of driving traffic to affiliate programs and get-rich-quick schemes (“Make six figures from home!!”, “20 easy steps to top profits!!”, etc). This includes multi-level marketing (MLM) blogs and pyramid schemes. To be clear, people writing their own original book, movie or game reviews and linking them to Amazon, or people linking to their own products on Etsy do NOT fall into this category. http://en.wordpress.com/types-of-blogs/
I am sorry, but advertising is not allowed on free hosted WordPress.com blogs. The only exceptions are for high traffic blogs that qualify for and are accepted into the Ad Control program, and very high traffic blogs that qualify and are accepted into the paid VIP hosting program.
If you require an ecommerce site, advertising and/or affiliate links on your blog, you can hire a web host and get a free software install from http://wordpress.org In that case, please see the information at the link below to learn about the differences between free hosted WordPress.com blogs and WordPress.org software installs for self hosting. http://support.wordpress.com/com-vs-org/