It's a possibility, but I doubt it because for starters to be counting up to 35 daughters is rather silly. More importantly though it doesn't fit Sanji's profile. I refuse to believe that Sanji's family are Celestial Dragons, but it's certain that it's an influential one. The nature of their influence is simply not clear yet. And as in all families of such standing securing their lineage is important. Normally the first born child, and in most cases the first born son, inherits all. All the other children don't really have a nice prospect in life other than being back-ups for when something would happen to the eldest heir. There's even a term for these children, the so called "second sons" which encompasses pretty much all the children starting from the 2nd. Now these children have one other convenient use other than being an insurance and that's marriage. By marrying them into other influential families, both families become allegedly stronger due to an alliance strengthened by blood.
Now Sanji went from North Blue to East Blue at a very young age. Then worked as kitchen help on a ship that eventually sunk. After that he was rescued by a notorious pirate, but nearly died of starvation, and that same pirate then raised him for several years. Following that Sanji became part himself of a pirate crew that was led by one of the most atrocious pirates of the new generation. Under his command Sanji also obtained a bounty that is nearing the 200M. It also has to be mentioned that Sanji disappeared for two whole years.
If Sanji was the heir of the Vinsmoke family, it would mean he would be extremely important to them. Till now however no one gave a damn about him while they should be very well aware of what he has been doing, at least since he joined the Strawhats. Sanji just said it himself, that the person who arranged the marriage and edited his wanted poster are one and the same. So his family only started 'caring' when he's supposed to marry with someone. This all really brings forth the image of Sanji being one of the younger children of the family who got neglected because he was nothing more than a spare and as a result grew a rebellious attitude and tried to prove his worth on his own or wanted to get away. His family let him do whatever he wanted because it was too much of a hassle to keep in him check, but now that he is about to marry, they are going to make clear again who is in charge.
Also Capone said something interesting. He said that by default now the Strawhats would be under Big Mum. This is rather odd as normally the woman marries into the man's family, but in this case it seems that it's the other way around. Now if Sanji is the heir of his family, this would mean the Vinsmokes would also be under Big Mum, something Capone did not mention. So it makes more sense that Sanji is one of the younger children that the patriarch of his family is letting marry into the Charlotte family. As he is the black sheep of their family, they now got rid of him while making an alliance with another powerful family. Sanji would essentially fulfill the only purpose they had for him.
I do believe though that the Vinsmokes have been powerful for several generations. Brook's reaction in particular was interesting. Brook has been isolated from the world for nearly 40 years or something in the Florian Triangle. The fact that he got the chills by hearing the name, indicates the Vinsmokes were already famous in his own time and not in a good way. It's of course possible he heard about them during the time skip, but I doubt it.
