Welcome to the forum.
No, a typical hot-shoe flash will not work at higher speeds because that is a limitation of the camera.
There is a feature called high-speed-sync, where the flash fires several pulses of flash, which does allow flash at higher speeds but I'm not sure if that is a feature of the camera or flash or both. Have a look at the Canon 420/430 EX and 550/580 EX.
Also, keep in mind that typically, flash will freeze the subject. The actual flash burst is much faster than the shutter, so even with a shutter speed of 1/30, you can freeze the action with flash. However, you might also get some exposure from ambient light, which would be blurry at slower speeds...so you will actually get two exposures, one from flash and one from ambient light. You can use the shutter speed to control how much ambient exposure you get.
Flash is typically not used in sports photography. Either the flash is too far away or it will distract the athletes. A better way to go, is a fast lens (big maximum aperture) and fast film/high ISO. Try setting your camera to AV, use the widest aperture (low F-number) and crank the ISO setting up.
If you only have the 18-55 kit lens, consider getting a faster lens. The 50mm F1.8 is the best bang-for-your-buck at less than $100.