I don’t see why not. They were featured several times on TOS/TOS movies. So they are definitely a familiar during that time period.
As far as looks are concerned... I am a little undecided about this. The different Klingon looks all had their place on the evolutionary scale of one series/movie to another. I guess I am going to wait and see how they are portrayed and go from there.
I do think the Klingons of the 23rd Century had a little more brass if you get my meaning. I think that edge will be an important element in their portrayal.