Thanks @Memphis_Raines, i find your post to make the most sense.
@pastymuncher hasn't taken into account the rest of his system is significantly more powerful with water cooling and his CPU is extremely overclocked, this takes up power. I think i'm safe getting a 2060s but not much more than that. I would have thought the 20xx generation would be more power efficient for similar power.
Just because it says 350w bronze psu doesn't mean it can deliver that much on the all important 12v rail. What make and model is it? The psu already seems rather small for that build with a GTX 1070. The game I am currently playing, Railroad Empire, is seeing my pc hit 298w and that's with the cpu and GTX 1070 at stock. Peak load can hit 368w with everything loaded up.
My water cooling setup doesn't draw as much power as you may think. The pump is only 23w, say 10w total for the led, flow and temp sensors and then 8x Arctic Cooling P14 fans that only draw 1.8w if running at full power but I have them running at 6v. My loop adds around 40w to the total power draw of my pc which isn't as much as people think a watercooling loop will add. You also seem to have missed the bit that I said my CPU and GPU are at stock speeds. I bet your 6700 with it's HT draws more power than my 9600k at stock. A GTX2060 super draws more power than a GTX1070, considerably more if it's one of the factory overclocked cards so that's another thing to consider.
Everybody is missing the point here. Just because the psu is marketed as a 350w model doesn't mean that it can actually deliver that much power on the 12v rail where it's needed. Take the
Kolink KL400w for example. This is a supposedly 400w psu but check the label and it only has a pathetic 264w on it's 12v rail. This is a worst case example and similar to a no name gemeric psu but it shows that you should ignore the headline power rating and actually check what the unit is capable of delivering across the rails. They have all done it in the past, Seasonic, Corsair, FSP, HEC and many others have all released psu's that have had significantly weaker 12v rails than their headline power rating so check and double check before buying what is argueably the single most important component in a pc.
Yes you could try drawing more power than the psu is supposed to deliver but this is a seriously bad idea. Power efficiency will be awful, temps will go through the roof so the fan will spin faster and make more noise and most importantly it will stress the components inside the psu. Those components will not be the best quality on a bronze rated psu and even some gold and higher rated so could result in a catastrophic failure which could kill the pc's other components if the psu's protection isn't up to scratch or doesn't kick in. It's simply not worth the risk.
The problem I have with the psu in the op's pc is that when I downloaded the pdf all it says is 350w bronze rated psu. No breakdown of what it can deliver on it's rails so I would be taking the side off that case and looking for a sticker on the side of the psu that shows the breakdown of power distributed across the rails. It is the only way to clear this up and until then nobody can say that it's definately enough power to drop a 2060S in.