Definitely true. For the record, ABM and RB said that the first season was "prologue" and that the "meat" of the story begins in the second. Specifically, they will explore issues regarding Rebecca's and Josh's relationship primarily, and examine both Paula's and Darryl's stories respectively.
Source: http://www.hollywoodreporter.com/live-feed/crazy-girlfriend-rachel-bloom-talks-884798
Source: http://www.ibtimes.co.uk/crazy-ex-girlfriend-season-2-showrunner-teases-ramification-rebecca-josh-greg-1556178
It is rather brilliant, resetting the whole first season's Rebecca - Josh dynamic with them as a couple. Of course, Rebecca's issues about abandonment, coupled with her obsessive tendencies, depression and Type - A personality should prove entertaining, especially when it seems that they will be doubling-down on the "crazy ex-girlfriend" premise.
I don't think the show will become "darker until the final season (season 4). I think that's when Rebecca bottoms out (she and Josh break up? Josh returns to Valencia?) and she is forced to face her issues. It wouldn't make sense for it to happen earlier in the series.