Yes you can put shoes in your dishwasher on the top dishwasher rack and wash the shoes.
I've washed shoes in a dishwasher before when I didn't have a washing machine in an apartment and it worked just fine.
I've even put shirts and pants inside my dishwasher and washed my clothes in the dishwasher on the top rack and it did an okay job at cleaning the clothes.
However a regular washing machine will get the clothes and shoes much cleaner however the dishwasher is better than no washing machine or better than washing the clothes by hand.
Just be sure to put the clothes or shoes on the top rack of the dishwasher to avoid the heating element melting the rubber soles of the shoes or burning through the clothes.