There's a lot of controversy on this issue, but if it works for your needs, absolutely do it!
Basically there's 2 questions you have to answer:
Should I use actual Arduino boards in production?
The answer is generally "no", simply because you need to customize the boards to add components to support your project, and to make them more robust. So, use an Arduino schematic as a guideline, modify it to suit your needs. The schematics are open-source, so follow the licenses and provide attribution to where your design stemmed from.
Should I use the Arduino build system in production?
The answer is generally, "yes", it works great and has tons of internal and 3rd-party library support. The Arduino core libraries are LGPL-licenses, which means if you modify them for your project, and put your project result into someone else's hands, you MUST release your modifications to the core to those who have your project result in their hands. But, you can keep your sketches and main bits of project closed-source if you wish.
That's the gist of it.