To put in a simple way. NO QSEE does not implement Trustonic's TEE APIs. However until recently Qualcomm SoC has support forTurstonic TEE e.g t-base-300 which probably is going to go away soon.
QSEE and TEE are parallel solution which provides Secure world. Qualcomm SoC have QSEE by default and it also has support for Trustonic TEE ( Trustonic TEE is supported via QSEE which is Truztzone implementation ). MSM8998 has support for TEE and i assume SDM845 uppcoming too supports unless QUalcomm decides to drop TEE support.