The answer can't be known. But the numbers are not reassuring. Based on data from the U.S. Energy Information Administration, it would take more than 70 years to replace the world's current electrical generating capacity with renewables including hydroelectric, wind, solar, tidal, wave, geothermal, biomass and waste at the rate of installation seen from 2005 through 2009, the last years for which such data is available. And, that's if worldwide generating capacity--which has been expanding at a 4 percent clip per year--is instead held steady.
This also doesn't take into account the amount of energy actually produced versus what is called nameplate capacity. Nameplate capacity is what a wind generator could generate if it operated at maximum capacity 100 percent of the time. But in practice, the turbines are only spinning when the wind blows and then not always at the maximum speed. This so-called capacity factor was just 27 percent for wind farms in the United Kingdom from 2007 to 2011 (PDF). For solar photovoltaic the number was 8.3 percent. Even hydroelectric stations ran at only about 35 percent of capacity. This compares to about 42 percent for conventional coal, 61 percent for natural gas, and 60 percent for nuclear power stations (PDF). The contrast is starker using U.S. numbers: 72 percent for coal and 91 percent for nuclear using 2008 figures, though natural gas was only 11 percent, probably because these were primarily plants that only come on to meet peak demand and so don't run very often.
What this means is that installing two to three times our current nameplate capacity in the form of renewables may be required to replace existing fossil-fueled plants. So, the transition period would actually turn out to be longer than what I've calculated, perhaps 140 to 210 years using 2005 to 2009 installation figures. Of course, installations of such renewables as wind and solar are accelerating. So, that would tend to shorten this longer transition period--as would leaving existing nuclear power capacity intact. But would we be able to shorten the transition period enough to head off declines in total energy production and prevent additional serious damage to the climate?