Can I accept a call on iPhone without manual intervention? I would like to know if I can accept a call without me or any person hitting the accept button?
It can happen immediately after receiving the call or after any number of rings, but automatic it should be.
There is an app called AutoAnswer, but it only works on jailbroken phones.  If you're into that sort of thing, you can find an article on it here:

http://www.ijailbreak.com/cydia/autoanswer-automatically-answer-specific-numbers-and-facetime-calls-on-your-iphone/