No, amateur telescopes would probably not give warning of a small object on collision course with earth, but they could monitor known, larger asteroids that professionals don't have the time to bother with, thereby catching unexpected changes in their orbits due to perturbations. They could also serve as a first line of defense for smaller object, near-earth passes, detecting new ones and providing observations which could be reduced to generate orbital elements for these bodies. If these prove to be potential hazards, larger telescopes could track them far out in case they might prove a danger during future approaches. Every impactor that has hit the earth probably had many near-misses before it finally connected.

The orbital elements of thousands of asteroids are catalogued, but many have not been observed in years, for decades, some not since their discovery! It would be nice if they could be occasionally checked up on and their numbers brought up to date. Many small bodies turn up routinely on patrol plates or on other types of searches, observers rarely have the time or the interest to follow up on them and it would be nice if they could send an email to an organization that could assign that discovery to an amateur who could then determine if it was a new or a recovered object. Other possibilities include comets, both existing and relict, which are associated with meteoroid streams.

A central clearing house coordinating amateurs could provide a useful auxiliary for any planetoid program. It could provide alternate observers if the dedicated telescopes were in daylight, or clouded out. It could match up appropriate telescopes with each object (it is not unheard of for some amateurs to have meter aperture reflectors, often backed up with advanced computers and sophisticated imaging equipment) and process observations for online publication. In addition to amateurs, this program could also be extended to college observatories whose instruments may now be too small for astropysical work, but still suitable for this application. It would allow excellent training for students and give a new lease on life to perfectly useable older instrments now being retired due to budget cuts or light pollution.

I would suggest you look up the American Association of Variable Star Observers which conducts similar programs with amateurs. Much of what we know about stellar structure and evolution can be traced back to raw data from routine observations made with backyard instruments. Some good science can be done with small scopes.