The short answer:
No, the Nine-Tails could not leave Naruto's body at will.
The longer answer:
Bijuu remain sealed inside of a jinchuuriki until either:
- the host loses control of the bijuu inside,
- the seal weakens, or
- it is forcefully extracted.
In the event that the bijuu is extracted, the original host typically dies. The Uzumaki clan has had a few temporal survivors of a forceful Bijuu extraction.
The specific example you reference for the Nine-Tails to be taken out of Naruto only really applies to female jinchuuriki; the seal is weakest during childbirth, and given that Tobi had attacked Kushina and Minato while Naruto was being born, extracting the Nine-Tails wasn't a difficult task.
Bear in mind that the seal between Naruto and the Nine-Tails really represented an ideological and metaphysical seal. The seal prevented the Nine-Tails from fully taking control of Naruto's body and will, and also prevented Naruto from fully influencing the Nine-Tails. However, after he had befriended Kurama and established mutual respect between them, the seal was no longer necessary.