Mac – Mac equivalent of DOSBox

I agree 100% with Adam's answer that DRM is a horrible thing, and "Digital Copy" in particular is a bad joke; see here.

However, I'll point out you can still watch your Up! Digital Copy on your Mac, even if OS X Lion doesn't support the PowerPC-based installer software on Disney's antiquated disc. I had the same issue and solved it as follows:

1. Launch iTunes.
2. Put the disc in your Mac's DVD drive.
3. In the left navigation area, select the disc.
4. You should see a page on the right asking you to Enter Code. Enter the unique activation code that came with your copy of Up!, then click Redeem.
5. Authenticate with your iTunes credentials, when prompted. (Assumption: You have an iTunes account, a working Internet connection, and your Digital Copy code is valid, not expired, and not yet redeemed.)
6. After authenticating with iTunes (the service), iTunes (the program) will proceed to copy the now-authorized movie content from your Up! "Digital Copy" disc to your Mac.
7. Find the new title in your "Movies" library. Watch it on your Mac^*.

All the details, including screenshots, can be found at:

• Apple Support - Transferring or downloading an iTunes Digital Copy.

* Worth mentioning:  Even after you get your "Digital Copy" into iTunes on your Mac, it remains protected and can only be played back on a device authorized to play back purchases from your iTunes account. Consequently, you may still prefer using another extraction method on the original movie, in order to yield a liberated version of your content unencumbered with such restrictions.

Summary: DRM is still a horrible thing, even with the workaround above.

(p.s. FWIW, this method also worked (for me) for non-Disney titles such as Dr. Seuss' Horton Hears a Who!, from Twentieth Century Fox, and Despicable Me, from Universal Studios. Mentioning this in case somebody else finds this answer but has a non-Disney disc; i.e. it doesn't seem to matter whether the "Digital Copy" is Disney or not, the above method should work to authorize & copy the content to iTunes.)

Quick answer: No.
Long answer: Yes, you can. You can run Snow Leopard in a VM (virtual machine) on your computer.

There are paid solutions like Parallels Desktop and VMWare, but a great free solution is VirtualBox. There is a fabulous guide on how to install Mac OS X Snow Leopard here

Note: You will need a version of Mac OS X Snow Leopard to install on the Virtual Machine. If you don't own it, Apple is still selling it here.