Yes, it is possible for the new ranks to be worse than the old estimated rankings.
When your site's metrics are certified you can choose to base your site's rank on the directly-measured certified metrics in order to get a more accurate ranking of your website.
In some cases, your new rank will be better than your old rank and in some cases worse. The Alexa Rank compares your website against every other site in the world based on the number of visitors and pageviews to your site. If you choose to use Certified metrics to rank your site then the visitors and pageviews are measured directly from your website. If you don't use certified metrics to rank your site, then the visitors and pageviews are estimated based on data from our global sample.
Your rank may move up or down depending on how close the estimates were to the directly-measured metrics.
Here's how to configure which traffic rank to show publicly:
2. Select 'Configure Metric Display' under the site URL.
3. In the "Alexa Traffic Rank" section select either "Estimated Metrics" or "Certified Site Metrics"
4. Press "Save Changes"