Yes and no.
Yes, because illusion will make victims of the spell think that it's a true thing, so their mind will make them fill it (so they will be blinded by a too powerful light made by the illusion, they will be hurt, as psychic damage, if the illusion "hurt" them one way or another, etc).
And no, because if victims know that is an illusion (saving throw, Intelligence check, etc), it will do to them nothing (maybe an illusion that make deafening sound will make them not hear anything else but that all), and unreal damage could disappear (at least thing like blind, deaf, paralysis, etc).
The only way that illusions can do real damage is if they are shadow spells (for D&D 3.5e, not sure that it exist in D&D 5e) or if victims believe so much in the effect that it appeared one way or another (like Phantasmal Killer).
I base myself on the second part of Phantasmal Force's description (PHB, p. 264), because it make sense that it's the same for other illusion spells:
While a target is affected by the spell, the target treats the phantasm as if it were real. The target rationalizes any illogical outcomes from interacting with the phantasm. For example, a target attempting to walk across a phantasmal bridge that spans a chasm falls once it steps onto the bridge. If the target survives the fall, it still believes that the bridge exists and comes up with some other explanation for its fall—it was pushed, it slipped, or a strong wind might have knocked it off.
An affected target is so convinced of the phantasm's reality that it can even take damage from the illusion. A phantasm created to appear as a creature can attack the target. Similarly, a phantasm created to appear as fire, a pool of acid, or lava can burn the target. Each round on your turn, the phantasm can deal 1d6 psychic damage to the target if it is in the phantasm's area or within 5 feet of the phantasm, provided that the illusion is of a creature or hazard that could logically deal damage, such as by attacking. The target perceives the damage as a type appropriate to the illusion.
I would do this way as a GM because their is no clear rules about it (as far as I know, I might be wrong).