What would happen if my computer shuts down while BitLocker is encrypting my OS partition?

I found this: BitLocker Drive Encryption in Windows 7: Frequently Asked Questions

According to Microsoft TechNet, you would be just fine.

This happened to me. I hard-reset the computer half way through decrypting, and when Windows came back up, it tried to resume decryption. It failed almost immediately with an error saying to run CHKDSK /R. After running that, the BitLocker decryption resumed and completed, without me even needing to restart the computer. There was no data loss, and I didn't have to repair anything besides the CHKDSK repair.

It would partially corrupt your disk, nothing less, nothing more. It's important to defer the process before shutting down/restarting, gracefully or otherwise, as otherwise quite literally half your disk will be encrypted, and half won't. That's not a good situation to recover from, especially since it will be likely encrypting on the fly whilst it encrypts the partition.