Not in the way you're thinking, no.
Any Real Server [0] in a datacenter will have some sort of "lights-out management" hardware used for remote access to that server. This stuff is known by a handful of acronyms, but I'll stick with "IPMI" because I like it best. This IPMI hardware is -effectively- a second small PC built into the motherboard. It will pretty much always have its own NIC... and I think I've seen versions that have their own physical ports to attach a monitor, keyboard, and mouse.
What exactly you can do with it varies from vendor to vendor, but -if your IPMI user account has the correct permissions- you are nearly always able to change "BIOS" settings, power cycle the server [1], and attach a virtual keyboard, monitor, and mouse so you can manage the server as if you were standing next to it in the datacenter with a crash cart plugged right in. Every IPMI system I've used also allows you to cause CD/DVD-ROM or floppy disk images on the PC running the IPMI client to appear as if they're loaded in a physical CD/DVD/floppy drive attached to the server.
The way these get set up is that their NIC gets plugged into the datacenter-managed switches, the port that NIC is plugged in to is programmed to be on a "management" VLAN separate from client traffic, IP addresses and access credentials for the IPMI device are set up, and the datacenter staff tell their customer what they need to know to access and use the thing. On a properly-configured network [2] it's not possible for software running on the server being managed to access the IPMI device.
It wouldn't be unthinkable for software running on the managed server to attack the IPMI hardware and be able to gain control of it, but these things are widely deployed and expected to manage hardware that's running potentially-hostile workloads... they're going to be fairly well designed and hardened.
[0] ...that is, not some Mac Mini or desktop machine that someone's paying to have colocated...
[1] ...whether that be an ACPI-initiated shutdown or reboot, or a hard poweroff or reset...
[2] Somewhat-related discussion here: <https://news.ycombinator.com/item?id=49862136>