Shutting down machine while deleting large snapshot
No you can't! The process of deleting the snapshot actually consists of committing the changes that were made in it. ESXi won't let you change power state during this process (forcing it off by taking drastic measures could corrupt your disks)
You can start the process with the VM off but this will only make it quicker if the VM has heavy IO. The downside to this is you can't start the VM part way through either.
If your snapshot is old it will take a long time. Avoid this by using only using snapshots temporarily and removing them as soon as possible.