Interestingly the doctor who diagnosed me said she very much wanted to get me to do an intelligence test because she was very interested to see what it would say (she thinks I have very high intelligence) but the clinic didn't have the licence to one in English.
I have never done a proper IQ test but I did once out of interest do an online sample quiz to join a MENSA organisation and got 98%.
OMG, I could have written your post 3 years ago when I first found out about ADHD. Interestingly, though I had always thought of myself as prone to depression/suffering from depression multiple times since I was 14 (in hindsight, this was just when my ADHD started to seriously affect my life because it was when I first had to start being responsible for myself.) When I started psychotherapy/CBT my therapist asked me some questions about my depression and actually I don't, and have never, fitted the DSM criteria for it. That astounded me. Similarly for anxiety.
The thing is that the feelings I've had which I always mistook for depression are feelings of despair at the way I can't seem to do things like other people do, that I have dreams and stuff but can't seem to get going on anything even when it's something I like, that I always self sabotage, that I genuinely forget things which are really important to me and feel like a horrible friend/person. The thing is in my case, these are proportionate reactions to situations which happened because of my ADHD, which I couldn't control. It wasn't that I felt like a useless person or a bad friend out of nowhere. I had evidence for these beliefs and they were (somewhat) rational.
It is of note that since I have been taking this seriously and been diagnosed I have not lapsed into depression. For a really long time actually. I think it's because I can now put things into context and understand why they happen. I do still have days where I feel totally lost and like I'll never be able to do anything but then I think about what I've achieved with the problems I have and I remember that it's not so bad. I don't get stuck in it like I used to.
They say that after diagnosis/discovery there is a period like grief with all of the different stages - anger, denial, depression, etc. And going through that stage of thinking of all the things you have missed out on is a hard one. I felt like writing to my college tutors to explain in case it helped them with a future student, but I decided not to in the end (not now, anyway). Being a part of the ADHD "community" has actually helped me to see things in a different way and a lot of the time I actually feel better about it now.