Yes they would all have the same Friedberg Number.
As to the consecutive serial numbers or even unusual serial numbers, most Currency Collectors that I know that are collecting by the Friedberg Number system don't care much about the note serial number, yes it's nice to have an unusual or even a low serial number but it's just about impossible to build a Currency Collection by Friedberg catalog numbers that way.
There are many different ways to collect currency.
You can collect by size, large or small, or both, then by type such as Silver Cert., Gold Cert., FRN, etc. or by denomination such as $ 1., $ 2. $ 5. and on up etc., then by year series such as 1934, 1963, etc. or collect all of the above like I do.
It's really a personal thing, collectors usually collect the way they want, not the way someone would like them to, if all a collector wants to collect are consecutive serial number notes, more power to them, some may only collect star notes or low numbers, I would bet their collection would be very small and somewhat un-organized but it's their collection no matter how small or large it is.
Thanks The Bill Collector. It is very helpful insights.