In a word, yes.
A greenhouse or greenhouse operations may be certified as organic. In fact, organic greenhouse vegetable, herb and flower production is a regular and popular practice by certified organic farmers and market gardeners, and in many cases the greenhouse vegetable business is considered highly competitive.
A USDA certified organic greenhouse must follow all the same National Organic Program (NOP) standards and rules that other organic farming operations must follow. In most cases, running an organic greenhouse vs. a conventional greenhouse varies little in relation to greenhouse technology, but there are special considerations, such as pest control and fertility practices to think about.
To get certified organic, whether setting up a new organic greenhouse operation or transitioning an existing greenhouse from conventional to organic, the steps are much the same as other organic certification processes.