Does the Piper PA-28 Cherokee wing have laminar flow behavior?
Short answer: Yes. You would see laminar flow.

Longer answer: It depends. In case of the wind tunnel it depends on the laminarity of the wind tunnel: Older designs had too much turbulence to allow for much laminarity. It was precisely for that reason that laminar flow was not well understood in the first decades of aviation.

The airfoil on the Cherokee is the NACA $65_2415$, and its Reynolds number in normal operation is in the single digit millions. The laminar bucket is ideally between the lift coefficients from 0.2 to 0.6, and the Reynolds number is low enough to allow for laminar flow. When you approach stall, however, the upper side has a pronounced suction peak near the nose which lets the flow rapidly transition to turbulent flow right after the peak. Laminar flow can only be found on the lower side (if surface roughness is low enough).

The pressure distribution over the rear 50% of the airfoil shows a constant pressure rise, so the onset of stall is marked by flow separation which starts at the trailing edge and slowly marches forward with increasing angle of attack. This leaves the suction area in the forward part unperturbed and keeps lift nearly constant around stall.

Contrast this with the stall behavior of the 5-digit NACA series, which can only be described as nasty. Stall is marked by flow separation right past the suction peak at the nose, and the lift coefficient suddenly drops by at least 0.2 counts when the airfoil stalls. Only some laminar airfoils have a similarly harsh stall behavior; this happens mostly when their designers were too ambitious and achieved the pressure rise with a Stratford pressure distribution. This is a distribution which keeps the separation margin constant along its length, and at stall it is exceeded everywhere at once, creating a sudden, large separation.

A well-designed laminar airfoil has a gentle stall behavior. Its lift coefficients with laminar flow are normally quite a bit away from stall, and its stall characteristics can be tailored independently from the region with laminar flow. Using a NACA $65_2415$ instead of a NACA 23015 is not a marketing gimmick, but a sound choice.

Regarding the performance: As long as the plane has a fixed landing gear, the laminarity of the wing will have little effect on top speed - the parasitic drag of all those things sticking out from the airframe will dominate drag. In addition, the higher the Reynolds number in flight is, the shorter the laminar flow will be before it transitions to turbulent flow, so the effect is much reduced at higher speed. Also, the way the wing is built makes a lot of difference, because every rivet head and every gap will create a wedge of turbulent flow behind it.