No they don't put resistors in vacuum cleaners and the surge shouldn't be that much greater with DC than AC
For sure it is.
In DC, surge is only limited by resistance who is very low to reduce losses.
In AC, current is limited by impedance, that's resistance AND inductance.
Inductance is high because we have the armature (more or less 1mH) in serie with two field coils.
As the air gap is large, this inductance normally do not saturate.
For this reason, surge in AC is readily low in comparison with surge in DC.
Vaccum cleaners are not intended to work with dc power grid.
They even often use a triac power control who don't work with dc voltage.
With surge overload, problem is not overheating, but bad comutation: you can have a "flash" between motor brushes, what can damage the motor.
Overload of more than four times the nominal current is not acceptable in a DC/AC universal motor.