Oh, its having an impact - in the 'west' at least. The game has been seeing shifts in its chart for longer than BO has been out though, but there is no denying there are fundamental changes in its chart over the past month. The like clockwork rhythm of the slope is getting disrupted.
https://steamcharts.com/app/578080#7d
Minimum players are really telling - usually the game bottoms out at 120K players (or more..or less), last night, it was at 25K, and stayed under 50K for a few hours, right during the 9pm to 1am EST (6pm - 10pm PST) times.
PUBG will remain solidly viable for a long long long time - depending on how Activision handles BO, if they make BR an annual release, PUBG might outlive Blackout but remain second fiddle to the COD BR of the year.