I'd seen an informal report of this in National Geographic. It certainly looks possible that F. drudeana is silphion -- the National Geographic article also went into its culinary merits, ahead of other species of Ferula, which the Plants article doesn't discuss -- but of course it's hard to know what kind of evidence could provide a stronger confirmation.

I'm somewhat concerned that the stalk of F. drudanea is much thinner and less bulbous than ancient silphion is described to be. On the other hand the juice ('pleasant-smelling odor but an acrid taste') appears to be a good match -- though I wish we had a description of its colour: the highest-quality silphion juice is said to have been somewhat red. And the physical appearance of the root and seeds are very good matches for the ancient descriptions. Ancient reports say the stalk was edible; I haven't seen any comment on whether the stalk of F. drudeana is good to eat.

I wrote an answer here two months back that went into some of the ancient evidence about silphion, but there's one point I emphasised there that the Plants article doesn't treat adequately, and that is that most of the ancient sources about silphion's properties weren't written until long after its extinction.

The only pre-extinction sources that we have are the Hippokratic corpus and Theophrastos. They're all very well and good, but most of the claimed medicinal properties, including the purported contraceptive effect, are attested only in later (post-extinction) sources. That doesn't mean those sources are worthless: some of their recipes doubtless come from older material. But even with the pre-extinction sources, ancient medical writers are prone to giving drastically bad medical advice. Just ... take the claimed medicinal properties of silphion with a large pinch of salt. Authors like Dioskourides claim all sorts of medicinal properties for every plant under the sun: most of them are nonsense. The report in Soranus carries more weight, though, as I mentioned in my previous answer.

Edit: afterthought

I'm not commenting as a 'historian', but I want to point out what I think are some flaws in the article (the original, not the National Geographic one). The author feels the plant is the same due to the black root bark and the opposite arrangement of branches. The 'opposite' arrangement is depicted on the cyrenic coin- but I don't think the ancients necessarily thought much about 'opposite' vs 'alternate'. If we take the coin to be a highly accurate depiction of the plant then we hit another stumbling block- the umbel bracts at the top are smaller than anything existing in Ferula.

Likewise, if a highly lucrative plant managed to exist at Greek colonies past the extinction date- why weren't those colonies selling it? Silphion was worth more than its weight in silver at the time. Also, I believe the only place that exported silphion was the original growing area, Cyrene. So how and why did it get to Turkey (it was also said to not grow except on its native soil, which some have interpreted as evidence it was a natural hybrid)