Yes, if the date of the DMCA notice and the fall in traffic overlap or are in the vicinity of one another (and assuming that everything else was constant) its almost certain that the drop in traffic is due to the drop in rankings of web pages.
Google has updated its algorithms to slap a site-wide penalty for a website receiving DMCA notices or takedowns. And they are implementing this very strictly.
Source: "Since we re-booted our copyright removals over two years ago, we’ve been given much more data by copyright owners about infringing content online. In fact, we’re now receiving and processing more copyright removal notices every day than we did in all of 2009—more than 4.3 million URLs in the last 30 days alone. We will now be using this data as a signal in our search rankings." -Amit Singhal SVP Google.
Snippet from an official blog post by Google. https://search.googleblog.com/2012/08/an-update-to-our-search-algorithms.html?m=1
You can visit this site to check if your site is penalised due to some DMCA notices or takedowns.
Also, check the date when you received the DMCA notice and refer to your Search Console to check your average positions(under the performance section) in order to be sure if both these events occurred a few days apart from each other.