Using iWork from the Up-to-Date Program on another Mac
Disclaimer: I'm not a lawyer.

There are two angles to this - the practical "Will it work?" angle and the legal "Is this legally allowed by Apple?" angle.

Short answers - it will work; but it's not legally sanctioned by Apple.

Will it work?


Yes, once you redeem the codes on the Mac App Store, these applications will be tied to your iTunes Store Account's Apple ID.
These apps will henceforth show up in the Purchases tab of the Mac App Store on every Mac that you have.
Assuming the other Macs you own run OS X Mavericks 10.9 (which is the minimum requirement for the latest iWork releases), you would be able to install the latest iWork on them.


Is this legally allowed by Apple?


This is a bit more difficult to answer accurately. I can only provide some pointers on the different aspects and will try to add a score to make it easier to understand (positive means it's legally fine and negative means it's legally not fine).
Score: -2

Apple tries to follow a "what's paid for with the original product" approach when it comes up with software releases and updates. This has meant that Apple has charged owners of older systems for things like enabling WiFi 802.11n, FaceTime on OS X, etc., while giving these free for purchasers of newer Macs (this is similar to newer iOS devices getting iLife and iWork apps free whereas older devices still have to pay for them). From this angle, no, you do not qualify to run this license of iWork that you have been given on other Macs you own.
On a related note, if you look at past up-to-date programs from Apple for OS X, for example, the OS X Mountain Lion up-to-date program, it clearly states


  The OS X Mountain Lion software content code must be used solely with the products that qualify for this offer.
  This offer is limited to one OS X Mountain Lion content code per qualifying computer purchased.
  

Score: 0


This recent article titled Apple Offering 'Free' Updates to All Owners of Aperture, iWork, and iLife; Not Worried About Unethical Users states that Apple has intentionally allowed users of older versions of iLife, iWork and Aperture (including trial versions or illegally acquired versions) to upgrade to the latest version for free. According to the unnamed source in Apple:


  ...With Mavericks, we have changed the way we distribute updates for legacy versions of our apps
  ...
  ...when Mavericks discovers legacy apps installed on your Mac, it provisions them as a Mac App Store purchase using your Apple ID. It saves us a lot of time, effort, and bandwidth. After the provision is complete, it will appear in your Mac App Store history as though you have purchased the Mac App Store version of the app.
  While we are aware that this enables piracy of our apps for unethical users, Apple has never taken a strong stance or action against piracy in the past. We like to believe that our users are honest, even if that belief is in vain.
  



Total score: -2 (against installing it on the other Mac).
To summarize, Apple's past bevahior and past terms state that this is not legally sanctioned by Apple. Even the article cited above states that "We like to believe that our users are honest, even if that belief is in vain."

So if you'd like the bitter truth, in my opinion, you are not legally allowed to install iWork from the up-to-date program on any of your other Macs that do not qualify for the up-to-date program, even though it would work practically.