No, not by any formula this site (or most brewing software) uses to calculate it — and the reason is mechanical, not a simplification. IBU measures dissolved iso-alpha acid, and alpha acid only isomerizes into that soluble, bitter form under the heat of an active boil. Dry hopping happens after fermentation, at room or fermentation temperature, with no boil at all — so there's essentially no isomerization happening, and essentially no measured bitterness contribution.
The number, worked through
2 oz (56 g) of a 13% alpha hop, entered as a dry-hop addition with 0 minutes of boil time in a 19 L batch at 1.055 boil gravity, computes to 0 IBU by the Tinseth formula — Tinseth's boil-time factor, (1 - e^(-0.04 x minutes)) / 4.15, evaluates to exactly zero at zero minutes by construction. Check this yourself — Rager's formula, notably, does not go all the way to zero at zero boil minutes (it computes roughly 19 IBU for this same addition under Rager's utilization curve), which is one of the clearest illustrations anywhere on this site of how differently the two formulas are actually built, not just differently tuned.
So why does dry hopping so obviously change how a beer tastes?
Because bitterness and hop aroma/flavour come from almost entirely different chemical compounds. Alpha acids need heat to isomerize into the bitter iso-alpha acids IBU measures; the essential oils responsible for a hop's aroma and flavour character — the citrus, pine, tropical fruit, floral notes described on every page in the hop reference — are volatile and largely driven off by a boil rather than needing one, which is exactly why late, whirlpool and dry-hop additions exist as separate techniques from bittering additions in the first place. Dry hopping delivers those aroma and flavour compounds directly into the finished beer without a boil to drive them off, at the cost of essentially no bitterness contribution.
The practical takeaway for recipe planning
If you're formulating a recipe and want a specific measured bitterness, that number comes entirely from your kettle additions — boil and whirlpool/hop-stand hops — not from anything added during or after fermentation. Plan dry-hop weight based on the aroma intensity you want (heavier dry-hop rates for a hazy IPA's aroma-forward profile, lighter for a more traditional balance), independently from your bittering schedule's IBU target — see how much hops for a 5-gallon batch for how that split typically works in practice. If your beer tastes more bitter after a heavy dry hop despite the calculator showing no added IBU, that's very likely perceived bitterness shifting alongside a much more intense aroma — a real sensory effect, but not a change in the actual measured bitterness number.