Yes & no. My spelling used to be pretty good back when I was writing regularly with pen & paper. These days I don't write, it's either typing on a phone or computer & my spelling is atrocious (for instance I just wrote "writting" & "atroscious"). The fact that I don't have to write in a professional (ug. proffessional) or academic setting, likely makes a difference too.
Hehehe. My spelling improved
dramatically once I started mostly typing. S'a lot easier to see and correct errors for me with a computer, and most of the errors these days are just finger fumbling (or intentional) rather than actually not knowing what the zog I'm spelling. Considering I was at one point diagnosed as learning disabled in spelling (and writing, for what it's worth), it's been a helluva' change. Typing saved my english/communication grades
Well, typing, online gaming, and fanfiction. Counter to what many would probably say would be the likely results of that combination, I blame the three for the majority of my gains in regards to written (and spoken, to a degree) communication over the years. Practice with intent towards accuracy/effectiveness and exposure to a massive amount of examples of both good and bad go a long, looooong way.
Though to the generational thing... no. Not so much. Seems to vary just based on non-age stuff -- hobbies/work activities, educational background (with most definitely no bias towards the older generations, ahaha, or if there is, the cognitive degeneration that comes with age offsets it), etc. Person to person thing rather than something you can meaningfully generalize out to a generational group. Sorta' helps on that front that
most folks seem to be honestly kinda' shitty at spelling :V