Yeah, vitamin C is ascorbic acid -- for acidifying things to a pH safe for water bath canning. Most recipes call for lemon juice for that. And I think there are old wives tales about crushed aspirin in pickles keeping them crisp, which may have resulted in the idea of crushed vitamin tablets.
but no, it's not going to thicken anything.
You can make many jams without pectin, though you have to be willing to cook them down a lot longer. I've done both grape and plum preserves without pectin and they turn out great. The deal is that they have to be a lot more concentrated, so they take longer to cook and they tend to taste more cooked.
if you go to the National Center for Home Food Preservation website, they've got a number of jam recipes without pectin. You do have to do high or medium pectin fruits to get it to work, however.