It's hard to not think it the interview had some effect:
1) We went from basically just speculation on the Eichel deal to legit insider leaks in the week leading up to the trade
2) Eichel himself said that the interview would be 'much different' if he hadn't gotten traded.
3) Hours before the trade, someone leaks to Weekes about Calgary's trade package.
4) The fact that the trade happened in the middle of the night hours before the interview happened.
Obviously we will never know the full story behind the Eichel trade, but it's fair to say that the interview represented some sort of deadline for the Sabres ownership/management group. There are no coincidences here, and a trade that took months to get to gets finalized hours before Eichel is sitting down in front of cameras? Even if the actual effect of the interview was minimal. The timing of the deal and the timing of the interview tell us they are somewhat connected, even if the degree which it effected it is up for debate
When we see the initial ask (Elite prospect, very good prospect, top 5 draft pick, and another 1st rounder) vs the reality of what Adams accepted (very Good prospect, Middle 6 NHL winger, a late 1st round pick, and a swap of a late 2nd/early 3rd), the Sabres were not content to simply wait out for their 'ideal' deal anymore. Obviously them taking that step to accept less than their asking price can't be put on the interview, it was the end of a very long negotiation between several teams over several months. However, it really seems the potential embarrassment of being dragged in the media by Eichel played a role in pushing the deal across the finish line.