Apparently you can. Because there is a startup doing just that. Super CFO is a Mumbai based startup which is offering CFO services for startups and SME's. 

Super CFO's business rationale:

Startups which are in growth phase don't require a full-time CFO and hence would like to hire an interim CFO or a virtual CFO. 

There is a special purpose CFO and an hourly service from the company. Super CFO doesn't reveal who its clients are. Bhairav Kothari is the founder of Super CFO and you can read his interview here. 

I am quite intrigued by the concept of outsourcing a CFO. I am not sure if outsourcing is the right word but that looks like the apt word. There is a saying that do what you do best and outsource the rest. And there is one more of focusing on your core strengths. 

Just like payroll, accounting and HR, finance is also not the core business or strength of any business. But is it outsourcable? A lot depends on the trust one can base on a company like Super CFO. But beyond trust how good does a startup feel about revealing all the financial information. After all any company's strategy is very well reflected in the finances.

This is nothing different from all the skepticism people are showing about cloud computing. The biggest detractor for cloud computing is security. How much can you a trust a third party vendor like Amazon, IBM or Microsoft with your data? What happens to the data which potentially sits on a foreign server in a foreign land? Yet companies are selectively choosing cloud computing and trusting these cloud companies with their data. 

Does the same hold good for CFO? Would you outsource your CFO operations?