Not likely all the way down at 12th place because it is very likely that a contracted participant will be ranked lower than 12th and it also depends on what bowls are hosting the semi-finals to help determine how low (in addition to contracts) they could be ranked and still get in.

Read the last bullet in this 2 page brief (before the table): http://espn.go.com/i/ncf/bcs/CFP_One_Pager_Cities_1.pdf

It states "Highest-ranked available teams will fill any other berths."

I got to that document from the official site of the CFP: http://www.collegefootballplayoff.com/

Some have detailed a similar quote to above that the highest-ranked teams WILL fill berths and not just be eligible for selection.

I pieced together some information in some other posts about how many at-large opportunities there are truly each year considering contracted games.
http://www.cougarboard.com/board/message.html?id=12345270
http://www.cougarboard.com/board/message.html?id=12345479

This was just documenting info as I read through the details. Below shows a synopsis of how many at-large there possibly are in each year with a guess at how high BYU would have to be ranked to guarantee selection.

2014-15 - Rose/Sugar as Semi-Finals (3-5 at-large) must be ranked top 7, possibly as low as 9
2015–16 - Orange/Cotton (3 at-large) must be ranked top 7
2016–17 - Fiesta/Peach (1 at-large) must be ranked top 5

Now based on history I don't have any faith that these guys (those that ran the BCS and now CFP) aren't going to continue to manipulate their criteria before selections are actually made. So this could all change to make it more difficult to get in before it actually happens but as it is written/reported today this is the case.

This also means that in years of the Rose/Sugar with the semi-finals (THIS YEAR) BYU has more opportunity than other years. So lets hope for a stellar year in this the first year of the CFP and NY6.