I was planning on going to Disneyland the weekend of my birthday and then I found out it is the same weekend as Gay Days. Is it worth the free ticket to compete with the crowds or will I be spending my entire birthday in lines? 

I would really go for the $69 gift card instead. Again, I have to reiterate that we were there just last year ON the actual Gay Days weekend of (10/2 - 10/5), and I think the ONLY Fast Pass we got the whole time was for Soarin'. When we arrived late Thursday afternoon, we noticed the crowds in DTD were heavier that night than we expected for a Thursday. We thought it would be a sign of things to come in the parks for the rest of the weekend, but in actuality, I think a lot of folks who wanted to avoid Gay Days crowds went to DLR before the weekend and then left, because Friday was not bad. Yes, it was crowded, but it is always crowded at DLR.
OP, you may have an image in your mind of it being so packed that you can't get on any rides and it was not like that when we went. We rode a bunch of stuff without Fast Passes - including the very popular HMH - repeatedly, we went to the TOTP on Friday night, we ate a late dessert at the Blue Bayou, we did Goofys Kitchen, we rode TSMM a bunch of times, etc. It was crowded but we would work with it! When we DID start to notice that the crowds were getting crazy was late Saturday into Saturday night. But in all honesty, I don't think those crowds exclusively had to do with Gay Days or the Utah conference or anything. I think that was due to all the Miley Cyrus birthday people piling into the parks for the event the next day - and I really doubt she will have that same event on the same weekend again this year, so that alone ahould keep the crowds lighter than they were last year, I would assume.