It will take a LOT longer...
The motor is at the same speed, there is 25% less heat applied.
If one looks at a psychometric chart, and does the calculations, and accounts for heat loss thru the dryer case, you get about 3X as long to dry.
Gets even worse for old dryers, where the NiCr wire has oxidized and gone up in resistance by 10-20%.
Had some 240 V appliances at the school once, needed to put auto transformers on the line or the workers complained about everything from clothes taking long to dry to water on the electric stove in big pots never even being able to come to a boil. (208/240)^2 = 75%
Maybe.
GD hit the nail on the head earlier, it will take longer to reach the "set point" temperature at the lower voltage, but exactly how long it takes to dry a specific load really depends on how much heat is needed to dry that load. Once the unit reaches set point it is just a matter of how much run time the element is needed to maintain temp, the drying time will still be the same if the set point is same either way. This comes down to design of the unit to some extent as well. If the designer made it based on heat needed at 208 volts, then running at 240 volts only gives you faster pre heat time, once up to temp the rest of the cycle is the same from the perspective of getting the clothes dry.
Most domestic units have a 120 volt motor and controls so that remains same either way. If the unit doesn't have a neutral, very possible it is designed for 208 or 240 operation if designed for North America anyway.
If designed for European countries, the motor will run at different speed if used on a 60 Hz system - if a typical induction motor. More modern equipment may not matter as they may have ECM motors. Probably more common with a washer then a dryer but I haven't got much experience with what is inside some of the newest dryers out there either.