I cannot prove it was Roku but I don't believe in coincidences. The day I signed up, added my credit card, and purchased Starz, Disney, and Qello, was the last day of low junk mail volume. The very next day, I received over 175 junk mail offers. It might not be Roku, but one of the apps I purchased. Other than signing up with Roku and making the purchases, I have no other changes.
I have no subscriptions directly through Roku. While a get a handful of junk mail I can't attribute it to Roku. I think you are more likely correct that it's one of the other services you started using. I recently signed up for CBS All Access, and didn't see any uptick in my junk mail. I would look suspiciously at either Starz or Qello (maybe both).
I might get an email a week at most from Roku themselves, and about the same from CBS.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.