No, you won't lose any performance at all.
The only thing that adapters can sometimes influence is visual quality (& max resolution/refresh, but you already know that part), but if you use a passive adapter or cable like the HDMI-DVI one I mentioned, then the digital signal should be literally identical.
My current 1080p monitor has connected to it:
- A DP to DP cable.
- A DVI-D (monitor) to HDMI cable.
- A VGA (monitor) to VGA cable, with a (active) DP adapter.
I don't notice any difference between them.
Active adapters are more likely to show a visual difference (because there's some conversion happening), but I have two VGA to DP adapters in-use and the visual quality on them both (different brands) is fine.