Yes, it not only could hurt, it will, in fact, without a doubt, hurt. Gg and every other show are legally forbidden from even *reading* spec scripts ("spec" = speculation/written on the speculation of even the possibility of being bought). The only shows that have ever had an open spec policy have been the various Trek series since the policy started during Deep Space Nine's existence otherwise ALL unrepresented spec scripts go directly into the garbage, no matter how good they may or may not be. If you try to submit a specific story idea, you will be precluding them from using that idea, even if they came up with it themselves the week before they ever saw your idea so that they don't risk being sued.
So your only choice would be to be a writer good enough to get an agent, *then* write a spec script for *another* show in the same or similar genre -- because, even when the legal reasons are no longer an issue because you've got representation, it's *still* often considered arrogant to submit a script for the show that you want to write for because you're coming off as if you think you can write better than they can.
So for Gg, you'd submit a script for something like Grey's Anatomy or Bones (for the romantic comedy -- I would recommend Bones because it's easier and for the pop culture references), House (for the sarcasm), Supernatural (for the family issues) or OTH (for the young gal target audience) -- anything that's currently on the air that shares at least one substantial thematic aspect with the show you want to try out for.
I apologize immensely for being so brutal about it, but there's really no way to sugarcoat it. This is all stuff I learned from reading Creative Screenwriting and Scr(i)pt magazines, the primary magazines about screenwriting for movies and TV.
-- Rob
Very interesting...
So if anyone has a really good idea for an episode, don't write it down and mail it to them, if the idea is good enough the writers probably have thought to put it in the series anyway.
Very true. But that's not to say that you can't ask them questions about natural opportunities for story threads, like, "Why is Taylor running the town council again when Jackson beat him in the election for Selectman two years ago?" Anytime you can ask a question about an existing story point is great because it gives them an opportunity to come up with the solution themselves if they feel they have the time within the show to do so. All that you can't do is give them a solution to the question.

-- Rob
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Season 8: Beacause I want to see Lauren have to deal with young children (and llamas) on Gilmore Girls, not Evan Almighty (although I'll watch that, too.)
Yea that was exactly my thoughts. What if they think up an amazing storyline then someone sends them a letter suggesting the exact same thing. If they air the storyline, the person who sent the already scripted idea will think the writer took it from them. Even if the person who sent the idea is totally ok with it being aired without any credit or acknowledgement, it would still be seen as a copyright infingment. To avoid that, the writer would of course scrap the storyline all together and we may end up losing big.

I think we might need to step up the voting believe it or not.. I was pokin around at the CW veronica mars forum and these people devoted a thread unlike the gilmore girls CW forum just to voting on eonline and these poeple are doing 1500 votes a day each or so they so.. but maybe we should kick it up to hour voting sessions.. I really wish we could know what the percentages were... this is frustrating.. Less importantly tho, Im pretty sure we'll win the tvguide one.. we're about tied right now and it'll keep going up.. but eonline is more important.. so how about.. everyones goal is to vote 1000 times before Friday.. I hope it's possible! I just got done writing a 6 page letter to Lauren Graham and to Alexis Bledel and Im gonna send them my picture in there too..I hope they get the letters.. I'll have my picture up on the site tomorrow sometime..
Keep up the good work everyone! I know we can do it! Goodnight all! Sorry I couldn't make the voting sessions.. I keep missing them by like 10 minutes.. by the time i check my e-mail , it's too late.. but Ive done alot on my own.. Maybe we should set designated times for voting?
Geez we do have to kick it up a notch, I keep on missing out on the 10/15 minutes of voting

I'm going to try and do it next time, if I miss out, I will do my own hour long voting! I'm actually going to do that now! Grr I hate the people at the CW boards, everyones a jerk, no one cares about the show even though they are on the GG BOARD!

Oh well, forget them! There are plenty of people who can do this with us. I am going to go pass the news on about the 15 minutes of voting every day!