No. In fact, those cups contain poisonous toxins (BPA) and coated metals, making them un-recyclable. In fact, Keurig publicly says their products are not environmentally friendly on their website:
Reducing the environmental impact of our packaging materials and brewing systems is a top priority for Keurig. It is a challenge to create a portion pack that is recyclable and delivers an extraordinary cup of coffee; however, Keurig is actively working to meet this challenge head on.
The K-Cup® package is made up of three main elements — the cup itself, a filter and an aluminum foil top. The polyethylene coating of the foil - as well as the process of heat-sealing the various elements - makes recycling difficult.
The portion pack composition prevents oxygen, light and moisture from degrading the coffee. Without the barrier the packaging materials provide, we could not maintain quality or freshness.
Also, see this post on the basic economics of regular brewing vs. Keurig brewing: