Yes. Plumbing codes require you to vent a bathtub drain, just like every other fixture with a trap. The vent lets air into the pipe behind the draining water so the tub does not pull its own trap dry. Without one, the tub drains slowly, gurgles, and can let sewer gas into the bathroom.
The rule that matters is distance. The pipe between the tub’s trap and the vent fitting is the trap arm, and code limits its length. Under the 2021 residential code as adopted by Dallas (Table P3105.1), a standard 1½ inch tub trap must reach its vent within 6 feet, sloped ¼ inch per foot. The International Plumbing Code uses the same figure. Figures of 42 inches online come from a different code that DFW cities do not use, as explained in how trap arms work.
A tub with no working vent pulls air through its trap instead. That is the gurgle you hear as it drains, and once the trap water is siphoned out, sewer gas has an open path into the room. A vent that exists but is blocked at the roof does the same thing, so the signs of a clogged vent look identical. For how the whole system works, see what a plumbing vent does.
Where a vent pipe cannot run up through the wall, the base codes allow an air admittance valve in some layouts: a one-way valve that lets air in but keeps gas out. Acceptance still depends on city amendments and the inspector, so it is not a guaranteed shortcut, and adding vent piping is usually permit work. One honest caveat: an existing tub that drains well, never gurgles and never smells is rarely a reason to open a wall.