I guess it depends if its the public or private face of Coventry it understand their love or hate of Wasps.
They don't tend to comment on Wasps too often nowadays anyway. However heard through a contact at Wasps that the arrival of Wasps has helped them quite a bit as it has increased the visibility of Rugby in the city with a lot of people going to their matches that didn't before, also believe it helps with sponsorship etc. So whilst there are some negatives, there are a lot of positives as well.
A closer working relationship between the 2 teams would be great for Rugby and the city.