You might want to just cut back on the amount of food you feeding the fish. Unless you have a bottom level fish, you don't want the food to reach the bottom of the tank. Over feeding is a major cause of poor water quailty.
To answer your question about if your fish will eat ghost shrimp. the answer is yes. How fast depends on how big a tank is, how much hidding place you can supply, number of fish in tank. You see shrimp are a natural food for most fish, and no matter how big of a tank you have, it is still a confined space (cage)with no way to escape. so eventuallly the fish will find the shrimp and eat them. There are a group of small cories that only get 1/2" to 3/4" long as adults. you may want to research them and get a school of 3. being they stay to the bottom of the tank you should be fine with overstocking but with a 10 gal tank is so imprtant to do those weekly 20% water changes.