Yes, multi-signature transactions can greatly improve security. But this idea of using a third party to write your transactions for you is a very, very bad idea. It introduces an additional point of failure for security: someone can break into their server, and make it start generating transactions that send coins somewhere other than where you said.
Writing software that uses this API would be negligence.
Someone can also break into your servers and manipulate your transactions. It's our business to run a secure and reliable service. Bitcoin infrastructure is fairly complex and so the probably that you'll miss something are pretty high. Isn't it better to focus on your own business rather that spend all your time and money building and maintaining the backend piece?
Then release/sell a library. Don't expect Bitcoin users (who, especially the early adopters, are almost tautologically more likely to distrust centralized services). Library code can be audited, and guaranteed to do what it advertizes.
Writing software that uses this API would be negligence.