Yes. Moreover, if you backup the system great, you get peace of mind, but management hardly cares. If you BREAK the system while trying to establish a backup, management cares and it's "your fault."
You have exponentially more to lose than to gain by experimenting with this at all. In this situation you should convey the risks, let the stakeholders decide if/who is going to address this, as it's their risk to take.
Doing even minor things that could distrupt the execution for any time (attaching debugger, installing packet sniffer that blocks network traffic for a sec or cause a packet lost, etc) could deadlock the application.
The only thing I would risk is copy/pasting the binary/executable that is running to somewhere else so I could try and decompile it. Anything beyond that is a nope.
You have exponentially more to lose than to gain by experimenting with this at all. In this situation you should convey the risks, let the stakeholders decide if/who is going to address this, as it's their risk to take.