Probably not. Bare necks seem to require two things, being pure for the NN gene plus an unknown modifier gene, which seems to be a recessive gene. This modifier gene is not too common in US stock- hence my "probably not" answer. If it is not present, then clean necks will not happen.
If you know the original stock has true clean necks then it is possible to hatch out some, however it will not come about as a direct result of breeding the small bibs to small bibs.
For example.. both parents large bibbed and both having the modifier gene *will* throw a few smooth necks. The only advantage to breeding small bowties is your chances at smooth necks goes up a little higher, if it's present. If not present, you'll get a whole batch of small bowties, including some that might have just one or two feathers on each side or have feathers on only one side(hipster style, maybe?).
It can be tempting to think those examples are proof it's possible to 'breed down' to smooth necks.. fell into that trap myself by starting a project with this goal for one line. Then I got new stock by egg trade that happened to have the modifier gene.. in this line, smooth necks showed up in all sorts of bowtie-bib combinations. None of the outcrosses with other lines produced clean necks.. however it did eventually show up in lines with "their blood" even if it never happened "pre-cross".