It's not advised because it means that the GPU itself will be in an undefined state.
The GPU itself draws power from both the PCIe slot as well as the PCIe power connector. These are two separate power "domains" that are isolated from one another.
The PCIe connector powers everything from the memory, the display outputs, the high power side of the GPU and everything else on the card.
The PCIe slot powers the PCIe bridge that sits between the GPU itself and the motherboard.
The reason for this split power domain is mainly so that signals from the motherboard are correctly referenced to their host power system and so are more reliably read. At high speeds this can be crucial. The same goes for everything on the graphics card, all the signals are sent between devices referenced to the local power domains. If you had a 3.3V signal sent from a device using one power source, and you try to read it using a device operating from a different power source then they may not have the same 0V reference point and so my see a different "peak" signal which can make it difficult to know whether what you are reading is a 0 or a 1.
As a result in electronics we try to keep signals referenced to their correct power systems. Hence the PCIe bridge on the graphics card works from the motherboard host power system and then buffers the signals across to the GPU power system.
If you do not plug in the PCIe power plug your GPU will only have a fraction of the device powered up, the PCIe bridge. This will mean that there is a device that is trying to communicate with something that isn't there. It could also be leaking power into devices that are not perfectly isolated and so could be in an indeterminate state.
Having devices half-powered, or powered in unexpected ways can be Very Bad. It can reverse bias some devices in odd ways, it can mean a device is permanently operating in a maximum power mode when it would normally cycle down very quickly after initialising its related components that are not coming up due to not having power. The PCIe bridge may end up "stuck" in some unknown state or loop of trying to detect the GPU.
In short it can cause a lot of undefined and unpredictable results.
You might be fine or you might not.
