If I complete this (High School Diploma - Online High School - Ashworth High School), is there any chance an American university will refuse to recognise it?
No problems I would think, its RA. But like we talked about in the last post, Excel would serve the same purpose. My kids attend a public school that has no accreditation and only has state approval. That is the same thing you get at Excel. What you need to do is shoot emails out to a few schools and ask if you can be admitted based on XXXX High school Diploma.
I also doubt it - mostly it is a check the box item on applications. However you may have to work extra hard to pass the social sciences test since so much of this is common knowledge to USA residents.