Can parents' involvement work things for the better in the teaching process?

I would say yes, parents' involvement can help in the teaching -learning process, if manipulated in a good way. Usually, parents do not understand the underlying principles for teaching and learning, so, this fact must be taken into consideration.Also, parents could be used as resources in certain situations.

I believe that education is a vehicle having four wheels:

1.Student

2.Teacher

3.Parents

4.Resources

Absence or malfunction of anyone of these will stop the vehicle of education. On the other hand, their proper working will move this vehicle faster towards the destination of success.

Definitely, parents and teachers should be a team albeit with different areas of responsibility. Supportive parents can be a blessing and can act as an extension of the learning process, likewise teachers can ensure that the "life" examples shown by parents to their offspring is reinforced.

Everyone one team - and anything less will lead to defect

Surely , imagine what would happen if a parent read a story to all kg2 students in one class.what is the impact on students?another example,a parent accompanies a group of students to a museuem where he worked before or have full knowledge about it.It will be a wonderful experience with a wonderful impact.A parent teaches carpentry and a software engineer teaches programming.Finally , it will be an ideal school with very knowledgeable students.

If you can get them  involved in your efforts and work as a team it sure will have a positive impact.

on the other hand if your efforts contradict or doesn't synchronize with their action it will make things worse as it will disorient the students.