Is this a good way of generating diverse solutions to a problem using a genetic algorithm?
The success (or otherwise) of your proposed scheme may well be highly problem dependant, so I would urge you to consider diversity-promoting methods such as 'niching' or 'island models' that have proved useful across a wide-range of problems.

Island models, for example involve partitioned populations that are evolved separately, with only occasional gene transfer.

More details on diversification methods can be found in the (freely downloadable) 'Essentials of Metaheuristics'