Basically what core image's purpose is to take the burden off the processor and put the graphics things as the job of the video card. But if you have Tiger installed on a computer that doesn't support it, then it just puts the burden back on the CPU like it used to, but like others said, you won't get some of the special effects thats built into OS X, and other OS X apps (droplet effect in Keynote for example).
The MacMini is for regular computer users who just want to browse the internet, check email, chat, use Office (or iWork), etc, but nothing huge like Photoshop, or FCP. So for normal usage, it won't be a problem at all.