Not if we use nukes or solar to power it.
Some care is involved in doing this so as not to wreck nearby ecosystems, but the ocean as a whole is big enough to absorb a brine flow.
So our actual consumption is far below even those 0.8%. But our problem with fresh water isn't necessarily that it's not enough but that it's very unevenly distributed and we tend to be very wasteful.
This being said how much desalination do we have to do until the brine (now 30% more saline than regular salt water) is significantly affecting the overall salinity of the oceans? Desalinating 0.2% of the ocean's water would give humans a 25% more fresh fresh water and the increase in salinity would be marginal.
Does anyone know if an increase that looks as minute as this (0.1% increase is salinity?) is actually a real danger to ocean life and/or currents?
[0] https://en.wikipedia.org/wiki/Water_distribution_on_Earth
There are other aspects of desalination that seem far more critical, like the ones related to efficiency and the scale of the required infrastructure.