Yes, even the cheapest non-basic economy fares are eligible.

I just booked two seats BOS-HNL-KOA for $280 per passenger in economy, called up to do the upgrade. At first the agent said 50k for BOS-HNL and 15k for HNL-KOA (the Flex rates), but then he said HNL-KOA would only be 7.5k (the Saver rate). So I transferred enough Amex points into each passenger's account to do 57,500 miles per passenger. There was some difficulty processing the upgrade but he confirmed the upgrade (and it was reflected online) and said the "offline team" would call me after it was ticketed.

Sure enough, about 4 days later, I got a call from Hawaiian, very nice woman says that it's actually only 50k because one upgrade award covers the connection too, and goes ahead with the reissue (miles deducted, reissued tickets emailed). The reservation had to be split into two records but it all worked out. Ultimately we now have 8k orphan miles in each account but we'll use them sooner or later.

Even at flex rates, this is a great use of miles. BOS-HNL is usually $2500+ one way in F (never below $1879).