But basically I'm wondering if a system is help back by the sinad, snr ect of the system's weakest link or if there is some sort of sum instead?
When you hear no hiss when nothing is playing and you have the volume control set to the position then you don't have to worry about the system noise floor.
Distortion at 1kHz at that specific set level is not really that relevant. The DAC might have that SINAD but the amp will most likely not nearly be at full power yet so distortion at 1kHz won't reach that of the power amp near full power.
Assuming since you seem to be a SINAD guy and thus distortion will be low it won't be a problem. Your speakers will 'f the 2nd harm distortion up to much higher values. Here's the thing though. The louder you play the more distortion you get from speakers but the less sensitive your hearing becomes for 2nd harm. (masking).
At normal SPL the system distortion will be dwarfed by that of the speakers and depends on the distortion of the speakers itself.
So... when you don't hear noise at your listening position with nothing playing, late at night (don't attempt during the day) with the volume control at or slightly above the 'comfortable loud' position then you can stop worrying about SINAD, noise etc.
As restorer John already mentioned the final numbers depend on so many factors.