No, that's why signed kernel+initramfs+LUKS+dm-verity: protect the boot process all the way into userspace where you do have network access. From there you can request the TPM signs messages with a preloaded key it will only allow using it if you went through the whole secure boot process. It's exactly what Android does with Play Integrity and the strong integrity flag.

That way you can prove to the server that the computer is still secured and untampered with up to that point, which means the script that deals with the periodic checkin should be running untampered as well. If you've secured down the Linux install appropriately, it should be impossible for the user to gain enough privileges to request the key again from the TPM or extract the data key out of the mounted filesystem. That also means you can trust the system to block mounting any drives, force VPN on, make sure your MDM runs, all that stuff.

You can reset the BIOS, boot from USB, all that stuff still, but then it would also wipe the TPM and so the OS no longer bootable, and obviously no signed TPM messages either so even if you find the script and how it works, at that point you don't have the ability to sign the messages so the server won't give you the data partition's key either. The moment you tamper with it, it breaks the trust chain and the keys are gone. Can't flip a single bit on the system and boot partitions without the checks failing.

It's not bulletproof, some laptops you can sniff the TPM bus in minutes due to design flaws, but in theory as long as the hardware holds it's pretty secure. And obviously you can always just take a picture of the screen, no avoiding that. But it puts enough hurdles it'll stop most opportunistic exfiltration. One bad move and you wipe the keys, so you better know exactly what you're dealing with or you have one embarassing and incriminating email to write to IT to have them reprovision the keys.