The short answer is no.
The longer is answer is... it may see a tiny amount. Digital cameras are designed to mimic the sensitivity of human eyes. Digital cameras have filters installed to block the transmission of UV and IR light from reaching the sensor. The filters actually improve the optical quality of the camera since different wavelengths of light focus at different distances after passing through the lens and since these wavelengths (which we humans cannot see but the camera sensor can see) are so different that they aren't even in the visible spectrum, the easiest way to fix the problem is to just eliminate them completely... hence the filters.
Without the filters, your camera would appear to take slightly "soft" images no matter how well you focus.
Some people modify their cameras and remove the IR filter to allow shooting in IR. This is a destructive process and of course involves voiding the warranty. So most people tend to do this with a spare camera rather than their primary camera.
If this is just something you need for a single project (you don't anticipate having a long-term need for an IR camera) then you could always just rent a modified camera.
LensRentals rents Canon and Nikon bodies modified for IR (sorry -- they do rent Sony gear... just no Sony gear that happens to have been IR modded.)