no are you crazy it will damage your hair it will mess it up so bad you have to cut it off just blow dry it or wait for it to dry hot water and cold water dont get along very nicely it like there fighting in a sprawl and then something messes up and you wish you never did it here is a tip if you love you beautiful long hair dont do it>
It can but it takes longer. And yes, you are damaging your hair... Your literally frying it.. Ever had a hot frying pan and put it in a sink full of cooler water and heard it sizzle and watched the steam rise? Basically when you straighten your hair wet your doing the exact same thing. You will hear it sizzle and see a ton of steam!
If i were you i wouldnt do it, but thats your choice. I ruined my hair and had a million dead and split ends.
It only take a few minutes longer to dry your hair first! Hope this helps :)