Can a six member ring expand to achieve octet completion to stabilize a carbocation?
The reaction which we are talking about here is called Tiffeneau–Demjanov rearrangement.

According to Wikipedia,


  the Tiffeneau–Demjanov rearrangement (TDR) is the chemical reaction of a 1-aminomethyl-cycloalkanol with nitrous acid to form an enlarged cycloketone. The Tiffeneau–Demjanov ring expansion, Tiffeneau–Demjanov rearrangement, or TDR, provides an easy way to increase amino-substituted cycloalkanes and cycloalkanols in size by one carbon. Ring sizes from cyclopropane through cyclooctane are able to undergo Tiffeneau–Demjanov ring expansion with some degree of success. Yields decrease as initial ring size increases, and the ideal use of TDR is for synthesis of five, six, and seven membered rings. A principal synthetic application of Tiffeneau–Demjanov ring expansion is to bicyclic or polycyclic systems.


According to The Encyclopedia of Reagents for Organic Synthesis (DOI: 10.1002/047084289X), the yield of your product will be around 40-42%:



You can check out the Wikipedia page for more details.