I feel it is dangerous to say I will do everything one way. So to say I will do all music I learn without pedal first then add it later might be ok in many instances, but could be devistating the next.
If you learn leggierissimo sections in Chopin concertos for instance, you will never achieve the quality of the sound if you dont use the pedal, and you willl never be revealed the touch required if you don't practice it with the pedal straight away. I guess we have to use our brains as to when we can neglect the pedal or not, but I generally would use it all the time, treat it as part of what you have to do, not something like the icing that needs to be put on later on, it must be integreated with everything.