It really depends on the team and the setup. Really, it comes down to how often the system goes down and how catastrophic it is, as well as what the response is after an outage. I have been in this type of situation before, but I always had nearly full control over the system, so any failure resulted in me creating some type of safeguard against future problems. This worked well: I had very few nights where I had to do anything.

Really, you should ask the people on this new team, not HN.