Assuming these non-accredited investors can afford the minimum investment but their net worth is not high enough to be considered 'Accredited' by the SEC...
You ask if CTA's can accept these funds, but CTA's are governed by the NFA/CFTC not SEC. You need to consult the NFA on questions with CTA's.
Hedge funds definitely don't allow non-accredited investors, if they are US citizens/residents. Some smaller advisors accept small net worth individuals.