I think it will destroy PROPER writing, if you use a lot of slang and shortenings of words. Ex: "hey sup? lol jk i dunno orz". However, if you write properly, it won't destroy good writing, but on the contrary help you develop your writing skills.

My students seem to think that using texting terms and symbols are suitable for formal English essays.

Nowadays more and more people use MSN or QQ,or things like that. Will they destroy good writing? I don't think so. In fact on the contrary, the vast majority of people who use social networks would probably have hardly ever written if these sites did not exist. Before such sites existed the average person very rarely put pen to paper.

Do you mean destroy instead of "destory"?