Yes, and my arguments for saying so are two-fold.
First, there's the historical timeline:
- When she first arrived there was jubilation
- Then some skeptics questioned the feat, their principal argument being a sudden increase in her speed overnight
- However an independent oceanographer concurred with that speed's being due to an unusual, favourable ocean current
- A week later she had a conference call with the expert skeptics, which left them satisfied
- IMO there was motive and opportunity for skeptics to press their counter-claim, if they had one, before or during that conference call: however, they did not do so.
Therefore the Preponderance of the evidence (at least) is that she didn't 'cheat' as was originally alleged by the skeptics.
Second, there's the current balance of opinion: the interested experts are now arguing over whether (because people in the boat would touch her ankle while she trod water, while helping her into her protective suit at night) it should be counted in the record books as an "assisted swim" or as an "unassisted swim". Therefore IMO there is no longer any expert doubt about whether it was "a swim" at all: which, was the question posed in the OP.
According to the video referenced below she has not yet published "the logs" of the swim, which one former skeptic (Evan Morrison) still awaits with interest (not so much because he still skeptical, but because he wants to learn from the details how she did it in order to improve his own techniques in the future). Although it's theoretically possible that further doubts may surface later, the same is theoretically possible for anything: because the question seems settled in the present time, so it seems appropriate to answer this question with "yes" now, instead of waiting forever.
http://www.miamiherald.com/2013/09/17/3633708/diana-nyad-cuba-to-florida-swim.html
Nyad and her support crew have quelled doubts and provided evidence in
recent days to show that she swam from Cuba to Florida under her own
power, without hanging onto or climbing into a boat or receiving
flotation assistance from the handlers, divers or kayakers
accompanying her.
Her evidence was allegedly sufficient to satisfy the expert skeptics:
http://news.yahoo.com/questions-linger-over-u-swimmer-diana-nyads-record-015309249--spt.html
"A lot of the big picture questions were answered," said Evan
Morrison, a San Francisco-based marathon swimmer and corporate data
analyst, who was on the call.
During that call, she appeared to satisfy other marathon swimmers with
her explanation that ocean currents had helped quicken her pace during
a section of the swim.
Evan said:
We heard from her navigator, who was essentially in charge of plotting their course across the channel given the gulf stream currents which is a fairly complicated task and one which I wasn't really qualified to even ask particularly complicated questions about.
The evidence
"Mitch Roffer of Melbourne-based Roffer's Ocean Fishing Forecasting Service Inc said he got an email questioning whether Nyad's swim was a hoax, so he decided to look at the charts for himself. What he saw convinced him that she could do it." (The Guardian)
Roffer said, "Many times that current runs west-east and you're constantly fighting the current if you're swimming north. In this case, it was in the shape of an S, and the angle was almost exactly from Havana to Key West". (The Guardian)
Roffer is preparing a report on the currents derived from satellites and ocean buoys. (Roffs.com)
"There's no hard evidence that Nyad cheated." (Business Insider)