A propeller not affecting the velocity of the free stream air would not generate any thrust (or drag), as the propeller works by the principle of creating thrust by accelerating a large mass of air, $F = m * a$.
The accelerated airflow from the propeller does generally increase the lift generated by the wing. The amount of lift increase depends on the configuration (how exposed the wing is to the slipstream of the propeller). This tends to be particularily noticeable on light twins:
(Image attribution: Wikimedia Commons)
There's also another effect on lift, coming from the corkscrew-shaped vortex of the propeller slipstream, perhaps more noticeable on single engine aircraft:
(Image attribution: FAA Pilots Handbook of Aeronautical Knowledge)
The image is a little bit unfortunate, as it demonstrates another effect as well (yaw from the slipstream), but you can also see how propeller slipstream will affect the flow pattern around the wing roots: on one side, it will tend to increase the effective angle of attack, leading to higher lift on that side, and on the other side it will decrease the effective angle of attack, decreasing lift on that side, leading to a roll-moment. This effect of course exists in twin engine aircraft too, but may be less noticeable, as the effect is more symmetrical, in the case of co-rotating propellers, or even symmetrical (in the case of counter-rotating propellers).