I'd hardly say the 'I have ...' structure is that rare and no average person I know would say 'I have swam'
I think a corpus study is probably about as objective a way as you'll readily find for determining how likely somebody is to know a word even if they do not use it. It's not the same thing, true, but it's as close as you'll get. Plenty of people here know "swum", it just seems that you move in circles that don't! It's certainly a help, but Word doesn't always get it right so it's worth trying to develop your skills so you don't need it to fill in gaps in your knowledge (it remains useful as a safety net, though!) That's for sure! It's said to be the easiest natural language to learn but the hardest to master.
I'd really like to believe that the average English speaker in the USA wouldn't say that. But since I see them saying: "He did did it." "That's when he had went...." "Did she began drinking again?" I'm not quite sure anymore.
