Do I stand a better chance of admission to an undergraduate business program if I apply early?
It all depends upon the undergraduate business program you apply to. For many, the timing of your application does not influence the final decision. The Admissions Committee will consider your candidacy in comparison to the total applicant pool, not only those who have applied at the same time as you. Apply when you feel your candidacy will be strongest - if that means you apply later rather than sooner, don't worry.
For other programs, there may be two to three application rounds per year with admissions done on a rolling basis. Applying early makes sense for these undergraduate business programs because applications are evaluated in the order of their arrival.
As well, keep in mind that if you would like to be considered for merit scholarships, you often need to apply early. International applicants may also have special deadlines to consider.