Answer:
It will depend.
Is there a close date or are applications being accepted on a rolling basis?
How many applicants applied? (I know you won't know this, but it can definitely have an effect on response time)
Does the company have a policy of sending responses to all applicants, or just to ones who are "interesting" in some way?
Are you a candidate that is so perfectly matched to the opening that whoever opens your materials will be in a huge hurry to call you?Or are you a marginally qualified applicant, or one who applied quickly or shoddily? Are you a serial applier?
Are you applying to a small company or a huge firm?