Yes, self diagnosis can be valid.

We live in a world where some autism "experts" think that there is no such thing as an autistic female, or that everyone on the spectrum was caught in childhood, or that autistic people never speak, or that all autistic people are either savants or completely useless, or that autism is an extreme male brain, or that only white people can be autistic. And in the USA, at the least, evaluations can cost into the thousands. Not that a multi-thousand dollar evaluation can't end with "You have some traits, but *insert group here* autistic people don't exist. It can. And free services for evaluation tend to be one of the following:

1. Nonexistent. Nothing to do here, unless you know how to create something that doesn't exist.
2. Specific to a group you aren't in. Might have an income range it caters to, and someone just above that might not be able to afford a paid evaluation.
3. Long waiting list. Cause there are a LOT of people who could use the dx, but can't afford the paid services. It can take months or years to be seen at one of these.
4. Biased. The people doing the evals here can have all the same problems that the "experts" have. 

So getting a diagnosis officially with a piece of paper and everything isn't always possible. It's also not always a good idea. ADA and anti-discrimination laws and all, discrimination still happens. An autistic man was denied a heart transplant largely because of his autism recently. A hospital said it wouldn't perform a kidney transplant on an autistic girl using a kidney from a matching relative who was only offering it to her. Autistic people get neglected, abused, harassed, killed on a fairly regular basis. Being diagnosed isn't always safe.

That doesn't mean that self diagnosis can't be done wrong. It can. Declaring yourself autistic after one internet quiz just doesn't work. Most of the quizzes are rooted in false stereotypes and theories. The Aspie Quiz is based on the idea that autism=neanderthal genes, last I heard. Besides the fact that correlation does not make a diagnosis. It just doesn't. For successful self-diagnosis, you need to understand the entry in the DSM. You need to understand what does and does not count as a clinical impairment, what is and is not a coping method which covers up a trait on the list, and what biases you and others around you may have. You should read what other autistic people have written about what being autistic is like, from all around the (not linear) spectrum. You should talk to autistic people about why you think you might be autistic (autistic people who are OK with self-diagnosis as a concept at the ones to go to here, by the way.) Research research research. Because it's not as simple as one evaluation. You need to somehow manage to evaluate yourself without bias after teaching yourself how to do an evaluation. It's not easy. But when someone does put in the work involved, yes, it can be valid. (Also a lot of these people wind up with a really good sense of if someone else is or isn't autistic, because they kind of just taught themselves how to evaluate for autism.)
I'd be just a wee bit of a hypocrite if I took a stand against self-diagnosis, since I was writing here as an autistic triple major for a couple weeks before I actually got a diagnosis. And I wasn't any less autistic during those couple weeks than I am now. I just didn't have a piece of paper that said my brain is wired the way it is. Which is a kinda sucky reason not to be able to talk about how your brain works, when you think about it. So while I will totally talk to folks who decide they are autistic on the basis of one internet quiz and no research to explain why that's not enough, if you do your research and conclude that you are most likely autistic, I won't be the one who says "NOOOOOO you can't be autistic because you don't have a piece of paper that says you are." I might be the one who takes the time to talk through why you think you're autistic while you're doing that research, if you decide you want to ask me for that, though.