Can a non notarized contract be contested?

Most contracts don't have to be in writing, let alone notarized, to be enforceable.  Of course, that doesn't mean that you can't challeng the agreement.  Non-compete agreements between employer and employee are scrutinized closely by the Courts and, depending on numerous factors (particular job, particular industry, length of restriction, geographical scope of restriction, employer's investment into developing goodwill, into training employee, etc. etc.) may not be enforced.