That depends entirely on what your speed control is rated for, and how it's actually limiting the speed of your router.
There are essentially 2 ways to control speed.
One is by lowering the delivered voltage to the device. In other words, turning the dial from 100% to 50% reduces the delivered voltage to the device to 60 VAC.
The other is PWM, which ALWAYS delivers full 120 VAC to the device, but switches it on and off really fast, based on a duty cycle. If the duty cycle is 2 seconds, for instance, and you set for 50% power, it's 100% ON for 1 second, and 100% OFF for 1 second. Most PWM circuits are much faster than 2 seconds, however. More like 20 times per second.
Here's where it gets interesting though, and I think you don't understand 240 volt circuits.
A 120 volt AC circuit has 2 wires - 120 volts, at up to the rated current, flows in one and out the other, switching directions 60 times per second.
A 240 volt AC circuit has 2 wires - 240 volts, at up to the rated current, flows in one and out the other, switching directions 60 times per second.
Notice that these are identical, except for the apparent voltage potential between the wires. This means that by applying your speed control to one wire of a 240 volt circuit, you don't get 50% to 100% control - There is NO 120 VOLT wire in a 240 volt circuit
You are throttling a 240 volt circuit from 0% to 100%
Essentially, if your router speed control is wired inline with only one of the wires in the 120 volt circuit (Which I wager it is), you could wire it inline with one wire of your 240 volt circuit, with the same results.
HOWEVER! Current capacity (ampacity) and voltage ratings change between 120 and 240 volts. It's imperative that you determine that your router controller is rated for the new load and voltage.
For instance:
A 120 volt 2500 watt element pulls 20.8 Amps
A 240 volt 2500 watt element pulls 10.4 amps
But, even if your router control is rated for the current, if it's not rated for the voltage, you're gonna let the smoke out - Or worse...