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If not how would I go about doing so? I know I sound like a newb and I am. This is my first PC game.
It doesn't remove it, but that should be no issue. You have plenty of time to finish your mission.
Just avoid wasting time with traveling and resting unnecessarily (using healing skill works much faster even if you fail most of the time) and you should be able to get the water chip much earlier than necessary.
I already found the water chip. From what I read at the vault there is an other time limit for beating the final boss or whatever.
I like water chips.
Once you return the water chip to the vault, there are no remaining time limits for the main quest. You can take your time and explore the world and your leisure.

And be leisure I mean frantically run away from raiders, supermutants and bandits until you pick up some heavy ordinance.
The time limit after finding the water chip is about 13 years, more than 10 times as much than in the unpatched version where you still had more than enough time.
I know you can finish FO1 in under 10 minutes (even 6 I think) if you know how, but I'm the person who likes taking it slow and exploring stuff.
So on my first run of FO1 I failed because of the time limit, if I would only had a few more days... that was frustrating.
I really hate time limits in games - it's limiting your playtime and product value.

It's like saying you got this huge world, but you got only a limited time to explore it.
In Fallout you have to find the waterchip quite fast, but afterwards you have more than enough time to explore everything.