|Image by Magnus Mertens in Wikipedia|
In essence, the question of whether mouth-breathing decreases risk of viral infections is based on the idea that contagious viruses spread via the nose by inhaling coughed/sneezed out water droplets infected with viral contagions.
Unfortunately, such viruses can also be spread if such droplets contact the eye. You have to imagine yourself moving through a "fog" of water droplets contaminated with viruses. Such movement results in your whole body, let alone your face, being contaminated with these infected droplets. That's why the constant reminder to cough/sneeze into your elbow to prevent airborne spread.
As such, the answer "possibly" since mouth-breathing only eliminates one possible way of catching a viral URI.
However, this simplistic answer only applies to certain, but not all viruses. The quoted 1981 research article upon which this answer is based on described an experiment in which the RSV virus was deliberately inoculated directly into the eyes, nose, and mouth of 32 adult volunteers.
The mouth inoculation did not cause infection whereas inoculation into the eyes and nose did.
However, keep in mind that different viruses have different ways of being contagious. The HIV virus is spread through sexual activity, hepatitis through blood, and more relevant to this blog, EBV virus (aka, mono) through saliva via mouth which is why this is also called the "kissing disease."
Furthermore, depending on the aerosolized droplet size, even mouth-breathing may potentially cause infection from the RSV virus if you manage to inhale into the lungs. Droplets that are small enough for people to inhale (either mouth/nose) are 0.5 to 5 µm in diameter and inhaling just one droplet might be enough to cause an infection. Although a single sneeze releases up to 40,000 droplets, most of these droplets are fortunately quite large and will quickly settle out of the air.
So, getting back to the question of what a person can do to prevent catching a viral URI...
Realistically, the best thing to do is avoid being around a sick individual and especially avoid enclosed, poorly-ventilated room crowded with sick people (i.e., subway car, bus, etc).
Beyond that if you don't mind looking silly...
• Wear swimwear goggles
• Wear a mask over the nose/face
• Wear gloves
• Thoroughly wash your hands before touching your face/eyes
More info and viral colds and flu here.
Infectivity of respiratory syncytial virus by various routes of inoculation. Infect Immun. 1981 Sep;33(3):779-83.
A Cold and Flu Risk That’s a Real Eye-Opener. NYT 11/14/16