Mediums,
I think ,"thinking" about writing to the man at the top is a good move and in some situations and industries it may be correct ,so I give you credit for thinking about it..
However not everything we think about we should act on..
It all really depends on your tone and content of the letter..
That is something we cannot judge on..
In this case though it has the ability to put more people offside with you than on your side..
All the best