A conflict of interest only happens in this situation if the person in question allows corruption on the roles.

I used to think you could not be. However I changed that to should not be, because I have known someone balance it very well with great integrity. 

Can it be done? Yes
Should it be done? Probably not.

Take a look here for more
http://adaptagility.co.uk/can-the-scrum-master-also-be-a-developer