I think it heavily depends on the kind of content you are consuming. I know it is anecdata, but my personal grammar and spelling skills went all the way up since I started using internet heavily (which was very noticeable to me, since english isn't my native language). And while I use a lot of incorrect grammar and spelling when talking to friends, I usually do it out of convenience (to shorten words, etc.), not because I don't know the proper grammar/spelling.
English isn't my first language. Yet, I believe my english grammar is getting worse even if I read a lot of English everyday. I blame this on globish though and the fact that it's relatively rare to get corrected on grammar mistakes around here.
On the other hand, the internet pretty much taught me English. Sure, we had English classes in school, but the internet gave me an immense amount of practical experience. Most of my peers, particularly those who didn't use the internet, finished school with significantly worse English than I did. Spell-checking has been pretty useful, but probably not vital.
N=1: I feel like - and I am 99% certain - that my grammatical and spelling skills have decreased since I started using the internet heavily.