Per the definition of what a Private Educational Loan is, I do believe that the loan mentioned would be covered. Now if they could shift some funds, then they might change the purpose of the loan, and if the purpose does not meet the definition below, then it would no longer apply.
12 CFR 1026.46 (a)(5)
(5) Private education loan means an extension of credit that:
(i) Is not made, insured, or guaranteed under title IV of the Higher Education Act of 1965 (20 U.S.C. 1070 et seq.);
(ii) Is extended to a consumer expressly, in whole or in part, for postsecondary educational expenses, regardless of whether the loan is provided by the educational institution that the student attends;
(iii) Does not include open-end credit any loan that is secured by real property or a dwelling; and1
(iv) Does not include an extension of credit in which the covered educational institution is the creditor if:
(A) The term of the extension of credit is 90 days or less; or
(B) an interest rate will not be applied to the credit balance and the term of the extension of credit is one year or less, even if the credit is payable in more than four installments.