Not only is the use of contractions inappropriate for a formal letter like this, it is also too casual to be used as a form of application for asking any favor. Also, the letter contains a lot of slang words like 'dough' and 'peeps', which can be replaced by proper words. This form of letter sounds too casual to be used for such a form of asking favors. So, it s false as not only the use of contractions make it inappropriate, the use of slang words also made it more appropriate for any official use.
