To be sure. TS does not require AIAG PPAP. It requires a product approval process. The CSR (such as Ford, published on the IATF / IAOB website) invokes the AIAG PPAP manual.
Any AIAG PPAP submission level requires you to do all the work. There is a table in the PPAP manual with R (retain) and S (submit) for the different levels. CSR usually defines the default PPAP level. Other submission level is only valid if you receive it in writing from your customer (authorized person, for example for Ford it is the STA).
TS allows another customer product approval process (such as VDA PPA).