No.
Section 5.7 of the Intel SDM is clear
Privilege level checking also occurs when the SS register is loaded with the segment selector for a stack segment.
Here all privilege levels related to the stack segment must match the CPL; that is, the CPL, the RPL of the stack segment selector, and the DPL of the stack-segment descriptor must be the same. If the RPL and DPL are not equal
to the CPL, a general-protection exception (#GP) is generated.
The rationale is that privileged code cannot afford to share a stack with unprivileged code for security reasons - each privilege has its own stack as defined in the TSS.
You can access the stack with a data segment register (e.g. through ds
), in that case one must have max(CPL, RPL) <= DPL (weakened CPL is still more or equally privileged as the DPL of the segment).