Do diesregarded entities file a form 7004 exgtension request?

When in doubt, read the instructions:

https://www.ftb.ca.gov/forms/2018/18_568bk.pdf

Extensions

California does not require the filing of written applications for extensions. All LLCs in good standing that are classified as partnerships have an automatic seven month extension to file. If the LLC cannot file its Form 568 by the return’s due date, the LLC is granted an automatic seven month extension unless the LLC is suspended or forfeited.

SMLLCs disregarded for tax purposes will follow the owners original due date and extended due date of the return.

However, the automatic extension does not extend the time to pay the LLC fee or nonconsenting nonresident members’ tax.

If the LLC is filing the return under extension, see form FTB 3537, Payment for Automatic Extension for LLCs, included in this booklet, to submit the required payments.

Rick

As Susan says, nope - for Federal.

But you should make sure the state (if applicable) doesn't require a separate extension.