I don't know how to tell whether certain hardware is supported by Parallels Virtuozzo Containers for Linux, Parallels Server Bare Metal or Parallels Cloud Server.
Driver support is included into the kernel:
# rpm -qf /lib/modules/2.6.32-042stab079.6/kernel/drivers/net/e1000/e1000.ko vzkernel-2.6.32-042stab079.6.x86_64
PVCfL, PSBM and PCS kernels are based on certain RHEL and CloudLinux distributives and therefore they support the same hardware they are based on. For hardware compatibility you should check corresponding release Hardware Compatibility List (further HCL). Truly supported drivers are the ones included in a kernel.
PVCfL 4.0, PVCfL 4.6, PSBM 4.0 are running on 2.6.18-* kernels and are based on RHEL5. For compatibility list you should check RHEL5 HCL. PVCfL 4.7, PSBM 5.0, PCS 6.0 are running on 2.6.32-* kernels and are based on RHEL6/CloudLinux 6. For compatibility list you should check RHEL6 HCL.
If your hardware is supported by RHEL (which means it's drivers are included in the kernel by default), but it still doesn't load ensure you are using the latest kernel:
on PVCfL and PSBM:
# vzup2date -m batch install
# yum update vzkernel vzkernel-firmware vzmodules