It depends on the SYCL implementation and the backend / target device.
Valgrind is not aware of anything that happens on accelerators. So kernels running on GPU won't work.
However, there are SYCL implementations that support executing kernels on the host as regular C++ code. This is usually called "library-only" implementation, because the SYCL implementation behaves like a regular C++ library in this scenario. In that case, all the usual C++ debugging and profiling tools like gdb or valgrind will work as usual with the entirety of the application, including kernel code.
This mode is supported in particular by hipSYCL/Open SYCL.
If you run on GPU, generally the native profiling and debugging tools from that GPU backend will work. For example, if you run your SYCL code through a SYCL implementation with a CUDA backend (such as DPC++ or hipSYCL/Open SYCL), you will be able to use NVIDIA's tools. This is because from the perspective of the tools, the SYCL application looks and behaves just like any CUDA application.
I'm not sure what you mean by "SYCL has its own profiler". SYCL is a standard and as such does not define any debugging or profiling tools. Some SYCL implementations may come with their own tooling.