Nope, OIS does not have anything to do with final image quality. It helps you get steadier shots without much effort which increases your chances of getting a blur free clear image.
The actual quality depends on the sensor, lens, processing algorithm and ISP.
Also the OIS used in Nexus 5 is only a 2 axis OIS which is inferior to the applications on Lumia phones and LG G2.
So do not judge photo quality based on whether a device has OIS or not.
Nexus 5 camera is worse than Note 3 in EVERY area.
GSMArena has this to say:
"The Nexus 5 camera certainly isn't going to win any photography contests - thanks to its poor white balance it can't even win its own 8MP league, let alone take the big guys with 13MP cameras (the Xperia Z1 and Lumia 1020 can't even be put in the same sentence with it). "
Among the 13MP camera flagship batch, Galaxy S4 has the best camera followed by Note 3. G2 has OIS but overall quality isn't as good as S4 or Note 3.