If Linux is installed in a virtual environment on my mac can I open apps that big sur blocks?
Yes, if you have Linux installed in a virtualised environment that you control on your Mac - then you could install applications in there. Restrictions on running applications within macOS using Apple's MDM system would not apply to applications within the virtualised Linux system.
Note that this all presumes that you have already got Linux up and running in a virtualised environment. If the owner of your laptop denies running most programs, they most probably also deny the installation of virtualisation software.