Usually yes. Cold working hardens the alloy, reduces ductility and leaves residual stress, so a solution anneal is normally needed to restore both the mechanical properties and the corrosion resistance — particularly resistance to chloride attack in the austenitic grades.
What cold work does to the metal
Cold drawing, rolling or bending multiplies dislocations in the structure. That is what raises the strength, and it is also what uses up the ductility: the same mechanism that makes the part strong leaves it with less capacity to deform before it cracks.
Residual stress stays in the part after forming. In a machined component it shows up as distortion when the part is later cut; in a corrosive service it shows up as cracking in regions that would otherwise be fine.
Why corrosion resistance drops too
In austenitic grades, cold work disturbs the oxide film and can leave the surface less able to repassivate. Chloride pitting and stress corrosion cracking both become more likely in the worked condition than in the annealed one.
Annealing restores the structure, dissolves the phases that formed during working, and lets the passive film rebuild uniformly.
Choosing the treatment
A full solution anneal is the usual answer: heat into the annealing range for the grade, hold long enough for the section, then cool fast enough to avoid re-precipitation. For the austenitic stainless grades that means a water quench or rapid forced cooling, and it means not lingering in the 425-815 °C band where chromium carbides form.
Precipitation-hardened grades are different: the sequence is solution treat, then age to the specified condition, and the ageing temperature and time come from the standard rather than from the shop floor.
Some cases want stress relief only, where full annealing would distort a finished part. That is a decision to take with the material supplier and the fabricator together, because a stress relief is not a substitute for a solution anneal in a corrosive duty.