From my experience, yes they will be paid.....eventually.
This creates a severe cash flow problem for military families, as they are paid on a monthly basis!
Actually, service members are paid on the 1st and 15th of each month. Otherwise, good point. Many military and their families (like many other Americans) live paycheck to paycheck.
They told us the same thing in the last shutdown in the mid 90’s. The Battalion commander had all the batteries come for formation before PT and informed us we will continue to get paid.