First off, I have several people I could introduce. I'd also like to know the industry you're operating in, what the data looks like, where it comes from, and how much it needs to be cleaned up if putting into a relational database, or if the better solution would be a distributed file system like MongoDB where you don't necessarily need to normalize the data. Also, if you're a startup, or if the company is well established with many existing customers and if this is for a new initiative.
It makes sense to have this person act as initial product and to derive the insights out of the data. They're pretty much the only person who can do this anyways, because they're the ones on the data. If you're in an early stage startup, I would recommend the strongest business owner (usually the early stage startup's CEO) be directly involved with this person on communicating what value your solution brings to clients, and what they pay you for, and in brainstorming on potential features and reports. Once the solution becomes established, and many customers start using it directly, there should be a different product person interfacing to those customers over time, gathering feature requests from customers and bringing it back to the Data Scientist/Analyst who spends their time working on the data.
Depending on whether the solutions are SQL or NoSQL or hybrid, there are different types of Data Science professionals you should consider:
1. Data Scientist
2. Data Engineer
3. Data Modeler/Analyst
1. The Data Scientist handles experimenting with the data, and is able to prove statistically significant events and statistically valid arguments. Normally, this person would have modeling skills with Matlab, R, or perhaps SAS, and they should also have some programming/scripting skills with C++ or Python. It really depends on your whole environment and the flow of data. In my experience, Data Scientists that exclusively use SAS are sometimes extremely skilled PhD level statisticians and focused exclusively on the accuracy of the models (which is okay), but often not sufficiently skilled to fit within an early startup's big data environment in today's world and handle all of the responsibilities you'd like them to handle described in your question. I'm am not bad mouthing SAS people as they are often the MOST talented mathematicians and I have a great deal of respect for their minds, but if they do not have the programming skills, they become isolated within a group without a Data Engineer helping them along. Often a SAS user trying to fit into this environment will force you to use a stack of technologies that a skilled Data Architect would not recommend using. It takes programming in some object oriented language to fit into today's big data environments, and the better Data Scientists are using hybrid functional and OOP programming languages like Scala. Extremely hard to find Data Scientist can also work with graph databases like Neo4j, Titan, or Apache Giraph.
2. The Data Engineer, if you're dealing with a firehose of data like Twitter and capturing it into a NoSQL architecture, this is the person who would prepare the data for the Data Scientist to analyze. They often are capable of using machine learning libraries like WEKA to transform data, or techniques like MapReduce on Hadoop.
3. The Data Modeler/Analyst is someone who can use a tool like SAS, SPSS, Matlab, or even R, probably a very strong advanced Excel user, but likely won't be a strong programmer, although perhaps they will have a computer science degree and have some academic programming experience.
The most important thing to watch out for is someone who is too academic, and has not been proven to deliver a solution in the real world. This will really screw you up if you're a startup, and could be the reason you fail. Often, the startup will run out of money due to the time it takes to deliver a complete solution or in the startup's case, a minimally viable product. Ask for examples of their work, and specifically dig into what it is that they did for that solution.
I've tried to cover a pretty broad range of possibilities here, but it's best to talk in specifics. I'd be happy to discuss this with you in detail. To answer your question, is it perfectly reasonable for someone to handle all of the responsibilities described in your question, if you find the right type of person with the appropriate skills, and a history of success.