If I go directly to Sistine Chapel on early entry breakfast arrival, can I then visit the other parts of the Museum before going to the Basilica without having to exit outside?
Unless the Vatican Museum has changed its protocol, the Sistine Chapel is at the end of the walk through the Museum, meaning that you will be walking THROUGH the entire museum before finally arriving at the Sistine Chapel. From the Chapel, you can either exit the museum directly or you may be able to sneak past the gatekeepers whose job it is to refuse people access directly to the Basilica UNLESS they are part of an organized tour. Your bluffing skills may be valuable here, and I have done it successfully, but on other occasions I have had to exit the museum from the Chapel and walk the entire perimeter of the outer Vatican walls to the Basilica entrance. Good luck.
Yes, you can backtrack and see the other parts of the museum. Just bear in mind that you will be "going against the flow" of people making their way through the museum.
Its been several years, but it seems traffic was 'one-way' through the Sistine Chapel. ( i.e. you could not exit the way one enters the Chapel and go directly back to the Museum area). And as I was not looking for a way back to the museum it is possible its there but I did not see it.
Hopefully a more recent, or better informed visitor can provide an answer.
As Baxter22 said, yes, you can visit other parts of the museum after the Sistine. Just be aware that you'll be going against the flow.
In November 2016 we did exactly that - we reserved the first tickets of the day and RACED to the Sistine Chapel. We had been there before, but it was in 2007 and there was an insane ticketing system that year. (Only groups before 1PM or some nonsense.)
It was worth every breathless step. At 7:45AM there were 10 people in the Chapel, including us and the security guards. It was one of the most peaceful experiences I have ever had and it beat the crowded experience I had in 2007. On the way there I also got some incredible pictures of some beautiful ceilings. Yes, we had to go backwards to get through the museum, but since it was off-season and only 8:30AM, it wasn't bad at all.
Just a little tip. Allow enough time for all. There's tons to see.
Enjoy!
For us, if we had seen the Sistine Chapel first, everything else in the Vatican museum would have been a little underwhelming to see afterwards. It really depends on your personal interest, so you may feel differently.