Will a Contribution to an SNT Qualify for the Gift Tax Exclusion?

No. Such a contribution does not meet the requirements of the annual tax exemption. A trust would not meet this requirement unless it complied with the rules set forth in the IRS Crummey case (to qualify for the annual exclusion, a trust must give a beneficiary certain withdrawal rights, so-called "Crummey powers"). However following those rules would disqualify or reduce the person with a disability's benefits. 

Instead, you could transfer the $14,000 to an ABLE account set up for the person with a disability if that person was disabled before age 26 and no one else has made a contribution to the ABLE account. Your contribution would be tax-free.