No. There is a limitation in the maximum shutter speed for flash sync (about 1/200sec). Everything equal or slower than 1/200sec will work. For Canon systems the shutter is set to 1/60s in P mode but can be adjusted freely in Av mode together with the Cn functions.
There is an exposure meter in your camera, right? Check your manual to see where to find it and how to read.
I know there is the viewfinder EV meter. But what happens is that is always showing underexpose with the flash mounted because somehow the shutter speed is fix at 1/60. This is with A mode. That is why i am confuse as to how to know if the exposure will be right.
What makes you believing this? If your flash is a TTL model than the metering will be done also considering the flash settings and in return the camera will adjust the flash. Read
here for more information about flash.