Did Kenneth indeed time-travel?

There are so many answers already, but I thought I'd chuck my hat into the ring!

Firstly, some information on the background of the film. It was created due to this posting in the classified section of the Backwoods Home Magazine. So as it was posted here, it was always going to be used verbatim in the movie.

That might mean nothing, but it's worth bearing in mind throughout the whole process of answering the question. The inclusion of the line wasn't really up to the director so much as it was staying true to the real story.

The second thing to discuss is did he ever really time travel? This should be obvious to anyone who watched and paid attention to the movie, but in case it's not, this is from an interview with the director:

Throughout the movie, the relationships between the characters are the
central focus, rather than the actual time machine itself. I noticed
that the machine was so hidden you only get glimpses of it. Was that a
conscious choice to have the device in the background for most of the
movie?

Yeah. It really isn’t a movie about the time machine. And yes,
you do see a part of it very briefly in the middle, but it could be
anything. We all wanted to maintain the tension in the movie by really
bouncing you back and forth as to whether you believe that there’s
really a time machine or not at all. Whether it works or not is
another question, but I fell like if there’s a ping-pong thing going
on, if you believe it or you don’t, the paddles get closer and closer
and by the end you’re like, “Is it?” Then you get the answer to that
thing.

To me, the movie ends when Darius chooses to walk across the plank. I
think what happens after that is obviously a lot of fun. And
emotionally and narratively, the movie is over to a certain extent
after that scene, except for the fact that we don't get the answer to,
"Is this person crazy or not?" or "Is she getting off the boat with
the right person?" [Laughs.] That’s one of the reasons I think the
film could be a little too ambiguous to be satisfying.

The way it ends could arguably be unexpected. The whole time you're
asking yourself, "Is this real?" or "Is this just going to end up as
some lesson?"

Rock and roll. [Laughs.] I did one shot that would allow
us to change that outcome because the time machine was always in it
and that was always there, so it was just a matter of what happens
after he hits that button. It’s a series of making five shots there
that are different. In allowing that from technical stand points, from
having it being shot with a big, wide camera, we still could play with
it and do whatever we needed to do. It left that possibility there.

First of all, when I first brought the possibility up while we were
shooting, people were joking and the alternative ending was
preposterous at the time. But then you don’t really know what it's
gonna be like until you see the movie through. So when we were
actually able to see the way the film played out, I felt like that
ending was gonna work.

I love a certain kind of film, and because of that I almost felt a
responsibility for it to end the way it did. It became very clear at a
certain point where I just couldn’t do it any other way. It had to be
this way. If not, why did we sit through this hour and a half?

So I'm aware this is all just background to your real question, but I think it's important to give context to the film.

Now your real question: Had Kenneth ever successfully time travelled before?

The answer is that it's left ambiguous and totally up to the viewer to speculate. However, speculate many viewers have. Here is a fantastic thread over at IMDB completely devoted to it.

There are a few arguments in favour of either outcome. The usual argument against him having time travelled before is that he doesn't know he's saved Brenda - so how could he have done it in the past. However, other arguments counter this by saying his act of saving her didn't necessarily mean he knew her.

My views are actually rather brilliantly identical to a poster on the IMDB thread, so I'm quite happily going to quote from his text:

He has travelled before.... Follow me...

I can only speculate that the truth behind Kenneth and Belinda's
relationship is really a blend of both their accounts. It's easy to
see how a socially awkward man such as Kenneth could build up a
friendship to be more than it really was. Conversely it would be easy
to see how Belinda may have been more than friends with Kenneth only
to have her perception of him change. Therefore...

2001- a. He and Belinda are together, she is killed. (His given
account) HER ORIGINAL FATE.... A car struck the house she was in.

Intervention Future version steps in. She is NOT killed.

b. He and Belinda are just friends, he is crazy. (Her given account)
HER MODIFIED FATE.... His car struck the house she was in.

2012- He travels back, 1st attmept. He "knows" 2001 "A" to be true.
Living with grief and on the run, he develpos a time machine to fix
the past...

These efforts cause the events of 2001 "B". However he returns to
2012 unaware that his attempt at saving Belinda was successful and he
continues to live as if 2001 "A" was still in effect.

2012- He places the ad and recruits Darius. The film plays out just as
we see with her ultimately informing him that Belinda is still alive.

Let me edit this to say that I believe he was responsible for
Belinda's death in 2001 "A" and is striving to fix that. The account
of events he gives Darius is only a half truth in that he leaves out
his responsibility.

However, it's important to stress that the answer is entirely up to the viewer - exactly as the film makers wanted it to be. Remember, in this film time travel as a sci fi medium is much smaller element than time travel as an emotional one - the idea of rectifying past mistakes.

My advice would be to watch the movie and decide which storyline fits your interpretation of the movie best. There are good arguments on either side, but from my point of view, I like the version of events I posted.