No. Only a decedent's Will may be lodged with the Superior Court (California Probate Code §8200). If you're still alive, the court will reject the document for filing. You're better off keeping the original in a secure place such as a safe-deposit box, or fireproof safe.
If you keep it in a safe-deposit box, remember that many banks will seal the box, sometimes for weeks, upon notification of the box owner's death.
We generally recommend that you tell your Executor where you are storing your original Will, and your other estate planning documents. In some cases, we recommend giving a copy of your estate plan to your named Executor.
Still have questions? Call us (818.707.8200) to discuss your estate plan.
[For information only; may NOT be relied upon as legal advice.]