That is a good idea, however I feel like there has to be some way to make it so Greenfoot won't recognize any transparent blocks. If push comes to shove, I will most likely end up changing the blocks in some way, but for now I am going to continue trying to figure out how to get this to work. Thank you for the response!

The methods Greenfoot uses to check for intersecting of objects use the whole image of the actors no matter if there are transparent parts or not. You can write your own methods to do so and there is a pixel perfect collision scenario out there, but this can easily result in massive lag. If you want to have the whole tetromino to be one object, you need to change the object when a part of it got removed when a row was filled. I think this will be more difficult than separating the tetrominos into the four blocks and make them move and turn together properly.