No. Your application will crash in mysterious ways and you'll scratch your head for months unless you look to system logs and see: MCE on CPU #4, recovered from internal exception <insert details here>, or any similar hardware breakage log. It can be DIMMS, CPU, PCIe, thermal, anything basically.
Monitor your servers. If you can't verify that the foundation is sound, you can't trust anything on that system even if it's formally verified to be bug free.
Exactly, it's incredibly useful to see the environment in which the application operates and how it reacts.
E.g. does your application spike in memory usage as network latency goes up? How does the application react when /var fills up (you should have an alert for that).
What I've frequently seen, running externally developed applications for customers are applications that hasn't been designed with monitoring in mind, so until you can sort of guide the developers to add all the metrics you'd need, you have to rely on what the operating system can tell you, perhaps with whatever agents are available that particular programming language.
Monitor your servers. If you can't verify that the foundation is sound, you can't trust anything on that system even if it's formally verified to be bug free.