Absolutely I believe your idea is possible. And, like with starting a new business, the three keys are planning, marketing and financial management. I recommend that you work up an informal business plan to help you think through and research all the aspects of this new service line.
Fulfillment services are definitely a great way to grow your business. If you've outgrown your basement or garage but can't make the investment in your own warehouse, there are some great resources out there. Check out Sears Commerce Services' Fulfilled by Sears. They offer competitive pricing and no long term storage fees.