My band is recording an EP next week, and we are dropping $1200 on recording alone. That being said, I want my guitar sounding great. It is a Gibson Les Paul Studio.

My bass player and I were going to go to our local music store on Friday to get new strings put on while our action and intonation is all adjusted to get them in new working order.

We start recording Monday. Is this too little time to get the strings broken in? Do new strings sound the best?

This is going to be really pro, so I want everything right.
Whether new strings sound good or not is up to the player, but a week is plenty of time to let them break in.
New strings sound the best, IMO. I would also check all your gear for weak links. Make sure all cables are perfect and anything that uses a battery gets a new one.

Does you guitar stay in tune now? Why adjust action if you like everything?

Lastly, have a backup guitar... Even if you have to rent one.

Just my .02.

plenty of time

treat the engineer with respect, tell him what you want and listen to him, he has absolute power on whether your recording sounds good or not.

enjoy it making a recording is hardwork.
1200$? Agreed on the backup guitar. I suggest a Les Paul and something with a lighter tone. Remember less is more in the studio. That's all I really have to say.
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I think the guitar has only been set up once, or maybe not at all, since I got over a year ago, so I want the intonation set up again.

I have a cheap backup, but I have extra strings and I think the studio has a couple guitars too.

And we have been good to the engineer, except asking him for a better deal last week, but we are over that
Bring an extra set of cables with you, just in case. Oh, and if you have an EQ, set it to flat, like you would a live, the engineer will add "coloring" later...only the EQ, you can leave the effects like distortion alone if you use them.
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Unless you've messed up your intonation since it was done the first time (or changed string gauge) there's no reason to get it done again. If the sound of new strings is the sound you want then go ahead and change them the day before you record, but make sure to play a lot after you put them on. They need to be good and stretched. That goes for guitar strings, I know nothing about bass strings.
new strings ALWAYS sound the best. hell, i'd change the strings again before you started recording. i love the sound of new twangy strings so responsive and clean.