[DiogenesKynikos]

Yes, but historically, scientists ended up accepting the heliocentric model long before the first stellar parallax was measured.

The heliocentric model's parsimony (explaining many different phenomena, such as retrograde motion of the inner planets, with the fewest assumptions) and various supporting observations (such as Venus' phases, which rule out any strictly geocentric model), combined with a physical theory that grounded the model (Newton's laws) rendered any alternative implausible by the late 1600s at the latest. It would be nearly 200 years before parallax was first detected.