It's not going to solve anything because they are just taking money early that they will need next month.
It might seem attractive initially, but within a few months the status quo will have reset and those employees who were living paycheck to paycheck will still be living paycheck to paycheck, just now it will be day by day waiting for their accrued amount to increase.
I suspect as a company you could do well, but you aren't solving any problems for the employee. And you may find that as business pressure increases you'll end up exploiting them in some way because they are vulnerable and have little protection. It won't be long before someone on your board says something like "hey, we could make a bit more money if we start charging x% interest to get early access pay they won't accrue until next month. That's fair because we're taking the risk they might not accrue it all." And before you know it you are just as bad as every other payday lender out there.
This unexpected expenses thing sounds like poor justification to me.
And charging the company Vs the employee is no different. If you didn't charge the company they could instead increase the wages of their staff by the equivalent amount. You are just taking money out of the potential pot that goes to the staff. Staff costs is just a single line on our summary p&l which includes salaries and benefits.