Are there any benefits getting a monitor that supports colour management when I don't work in a colour managed environment?
You can do color management with a monitor that doesn't "support" color management. This is non-intuitive, but when we talk about a monitor that supports "hardware color management", what we mean is a monitor that can communicate with the computer in a way that any monitor calibration done using the computer can change the monitor's internal LUT automatically.
There's an article on EIZO's website about the differences in the calibration/profiling process between monitors with hardware color management support and monitors without hardware color management support. Talking about software calibration that changes the computer's output to offset variations in the monitors output, rather than adjusting the monitors controls via hardware support:
However, the merit of this method is that any monitor can be calibrated, not just monitors that support hardware calibration.
With a monitor that does not "support" color management, any adjustments to the monitors internal settings must be made by the user via the monitor's control buttons before running the software correction on the computer that only adjusts the output of the computer's graphics card to compensate for the inaccuracies of the monitor.
Most calibration/profiling software includes an option for the user to manually adjust the monitor's color, contrast, and brightness controls while the measuring device is actively measuring the monitor's output and displaying the measured output in one corner of the screen. This is the only way to adjust the monitor's internal LUT with a monitor that is not "hardware color management" capable. Once the monitor is adjusted as close as possible to the target, then the software does a very detailed measurement of the monitor's output at various colors and brightness levels and adjusts the computer's LUT that controls the signal sent to the monitor to compensate for variations from the target in the monitor's measured output.
With a hardware color managed monitor, the software does the adjustment by altering the monitor's internal LUT via the data connection between the computer and monitor.