What is the precise manufacturer and model of your power supply? And while you're at it, list your entire specs please.
Addendum: But to answer your question, yes, it's safe to plug in your graphics card to display web pages and such. But as far as gaming tests, I'd need answers to my above questions. When I had an air cooled 980 Ti, it would pull 200 watts on stock fan curve, and would only hit the 250 watt TDP if I turned the GPU fans up to 100%. And my cpu would add another 100 watts or so. My total consumption at the watt according to my Kill-a-watt meter was slightly under 300 watts, with a platinum efficiency power supply. Personally, I would not even consider playing games unless I had a top quality manufactured and model power supply, and I'd want to have at least 150 watts to spare.