Hi Marton! This is Megan from the SEOmoz Help Team. I'm so sorry that we're late to answer this question! If you have questions about our tools in the future, feel free to send a message to help@seomoz.org for a quicker response.
The crawler that we use for OpenSiteExplorer unfortunately does not crawl https at this time, but we do plan on changing this at some point down the line. Our campaign crawler, however, does crawl https, so you'll still be able to find out information like if your site has any 404 errors, duplicate page content, missing title tags, etc.
I hope this helps!