Yes. The Reichstag had been growing in influence over policy during the imperial period, not only participating in legislation but also overseeing the budget and the conduct of policy. However, it was hindered by a highly fragmented party system, in which parties sought influence with the government rather than trying to build a majority to become the government. However, right at the end of the empire, there actually was a short lived shift to parliamentary government, with the chancellor being responsible to the Reichstag and not to the Emperor. This took place by an amendment to the imperial constitution in October 1918. However, this was not really put into practice because of the revolution and proclamation of the Republic a few days later in November 1918.

I'm happy to answer follow up questions about transitions to parliamentary government generally in European countries.