Yes, intrusive interstitials for mobile searches can have a negative impact on your search engine rankings. On January 10, 2017, Google announced that is taking action against websites that displayed intrusive interstitials:
“Starting today, pages where content is not easily accessible to a user on the transition from the mobile search results may not rank as high. As we said, this new signal is just one of hundreds of signals that are used in ranking and the intent of the search query is still a very strong signal, so a page may still rank highly if it has great, relevant content” – source
The same applies to app install interstitials.