I am listed as beneficiary on one of my moms checking accounts. She has severe dementia. Am I able to access that checking account?

If you're a co-signer (co-owner) of the account, you could. It wouldn't be ethical, but legally you could. My dad made me a co-signer on one of my parents' accounts, so I could write checks if my dad was incapacitated. It's the account I used to pay his funeral expenses, but it's still my mother's money, not mine. (She has dementia and can't handle her affairs.) Even though there are no beneficiaries on that account, I know that once my mother passes away, the money will be divided between myself and my brother.

A beneficiary is a completely different thing, however. As others have said, a beneficiary only inherits the assets after the account owner's death.

You can access a "checking account" to pay checks for your Mom using her name, you as her POA, for her care and her expenses only, and no. I assume this is an account set up as POD which means "Pay on Death" to you. And that means exactly that. Upon the death of your Mom you will present a death certificate to the bank and it is done. You will have the money that day. If the account on the other hand is left in her will, it is distributed by her executor after her death.
Especially for a POA it is illegal to dabble in any of this money held in your Mom's name. It is hers until death. You have a fiduciary responsibility to preserve all of her monies and it is against the law to start distributing funds to yourself. You are accountable to keep meticulous records of every cent spent for your mother, all receipts, and IRS filings and etc until her death. At that time the Executor takes over.

Stop, no, don't do it, do not touch the money.

That money is your mother's money. You can no more use it than you could help yourself to any other person's money on the grounds that she doesn't need it and it's almost certainly coming to you eventually anyway.

I don't know if you have a range of other options, but this is only an idea - would your sisters be prepared to lend you money (of their own), using the funds in the checking account as a kind of informal, hypothetical security?

No. You aren’t entitled that money until your mom has passed away. You’re a “payable on death” beneficiary.