I got under 30 a few weeks ago (after a fairly intense week or two where I learned how to actually look ahead), and I've been cubing since last June or July.
So ~9 months to get an under 30 average. Keep in mind, though, I haven't spent a lot of time studying algorithms or training intensely, I'm sure you could do it in much less time if you did. I was still doing up to 2 algorithms for eOLL, up to 3 for cOLL, and 1 or 2 for PLL when I was around 30, with purely intuitive F2L.
Yes, I force myself to solve every puzzle I do before I look up how to do it fast. I figure that otherwise when people ask "did you figure out how to do that yourself," I don't have to say "no, I looked it up on the internet." Instead I can say "yes, and then afterwards I looked up how to do it faster on the internet."
My original method was so bad that it still takes me ~7 minutes to solve using it, and about 60%-70% of the time I have to give up and either start over or cheat and use methods I learned later.