Can a company not pay you your vacation if you give a 2 week notice?

Yes, if you do not have an employment contract guarantying you your vacation (or vacation pay on leaving employment) or specifying a notice period, your employer can do this. That's because without a contract, you are an employee at will; an employee at will may be terminated at any time, including after notice was put in; and the law does not require companies to pay out vacation unless the company has voluntarily adopted a policy of paying out vacation on separation of employment. Therefore, they can terminate you before  you get your vacation, and would not have to pay you for it unless that has been their voluntarily adopted policy.

Any employer I've worked for or with would do this--in the future, do not provide notice unless your ready to fired on the spot, which means do not do it while vacation is pending.