Is it possible that renewables can supply 100% of our energy needs?
Yes It is possible, Paraguay and Iceland have already done it.
Paraguay relies 100% on hydroelectric energy, where as Iceland relies around 75 % on hydroelectric energy and the rest is from Geothermal Power (also renewable).
I think at least 100 countries can rely 100% on hydroelectric energy (quantifying this based on the average precipitation per year).
Sources: Hydroelectric Generation and Average Precipitation per year
My point being, not only there is solar and wind energy, there are other forms of usable renewable energy. So the answer is, yes definitely, we go 100% on renewable energy and we should