Is a sheet of carbon nanotube so thin that it's invisible actually going to stop a bullet?

Glass also manages to let light through. Carbon nanotubes are very strong. To make them invisible you just have to get the structure right and have big enough pores in the net for the wavelength of light to pass through.

what are the odds Harry can keep such a wall up for more than three tenths of a second?

The wall is Harry magic and as thus not able to be simply canceled by Quirrell. It also doesn't take that long to grab the time turner and activate it. Probably less than a second.