Photosynthesis only occurs in the visible light.have a look at the absorption spectra of the different pigments involved in photosynthesis, you see that all these pigments absorb light between 400 and 700nm (from a diagram from here):
You see that the absorption spectra of chlorophyll a and b are located from 400 to 500nm and again from 630 to 700nm. The maxima for both molecules are different so that the light is used more efficiently.
The other three important light harvesting pigments involved in photosynthesis (in cyanobacteria and plants) are: Beta Carotene, Phycoerythrin and Phycocyanin. These use different parts of the visible spectrum (hence the different color of cyanobacteria), but they still only use the visible part of the light between 400 and 700nm.
The reason for this can be seen in the figure when you look at the intensity of the sunlight (plotted in black). All photosynthesis occurs in the area of the highest intensity. Wavelengths shorter than 350nm are efficiently blocked by our atmosphere, wavelengths much longer are not transporting much energy.
To shortly answer your question: If we could "switch off" all other wavelengths from the spectrum, there would still be photosynthesis on earth.