Can an FPGA connected to a CPU via PCIE access peripheral devices?
The PCIe spec defines that devices can address each other, yes.

Whether that actually works is another question. Several chipsets have access control logic that requires the CPU to explicitly permit that two devices talk to each other.

This makes sense from a security point of view: if the sound card could instruct the graphics card to display a password prompt, you might type your password into the wrong window and send it across the network, and since no one expected the sound card to have meaningful attack surface, fewer permissions would be required to access it.