How fast and how?
You might consider providing a "living will" document that keeps your clients up-to-date on where the $$$ are and how they access them. If I'm using something like this I would want to be sure I can make payroll the day after you vanish.
(Not a potential customer or cash management expert, prioritize accordingly.)
My best guess, not until OK'd by a bankruptcy judge. You may have a strong claim on the funds but so does Mercury --- hence the fact stated above that you can't withdraw without their approval. On the other hand, they may be able to withdraw without your approval. A bankruptcy judge is the only one who could override their claim and release these funds to you.
Remember, SVB was an FDIC bank. The reason depositors are able to withdraw money today is because of the quick actions of the FDIC.
If the client is the owner of record Mercury hasn't any claim at all.
Only Mercury knows the exact structural details but based solely on their statement above, they have significant control and claims that you can't easily override yourself.
I wouldn't count on this all being resolved quickly in the event of a bankruptcy.