Short answer: Yes. Under Rev. Rul. 2004-55 an employer may let employees elect, before the plan year begins and irrevocably for that year, to have the employer-paid LTD premium included in their wages. Benefits for a disability that begins in that year are then tax-free.
In Rev. Rul. 2004-55 the IRS approved a plan where the employer keeps paying the LTD premium but each employee may irrevocably elect after-tax treatment, meaning the employer adds that employee’s share of the premium to taxable wages on the W-2. The election must be made before the plan year begins and cannot be changed once the year starts. A new hire can make a prospective election for the rest of the year.
The plan year in which the disability begins controls. If the employee elected after-tax treatment for that year, the benefits come solely from after-tax contributions and are excluded from income under IRC 104(a)(3). If not, they are fully taxable under IRC 105(a).
The election covers the entire premium for that coverage, not a portion. The employer may let a prior election roll forward, or make after-tax treatment the default unless the employee elects otherwise. STD and LTD can be elected separately, and each is taxed by its own election.