The stock arduino bootloader is 2KB. With an ATMega with 32KB of storage, and the bootloader reducing that to 30KB, the current firmware for the ice tube clock is 30,660 bytes. Strictly speaking, that's less than 30KB (30,720 bytes.)
That's perilously close to the limit of what'll fit on an Arduino bootloader-equipped 328. However, it's entirely possible that 30,660 byte hex file was sized precisely that way to just barely fit.
As for flashing the ice tube firmware on there, were you talking about somehow converting the C into arduino-code and then uploading it, or just somehow using the Arduino as an ISP?
Red M&M, Blue M&M: They all wind up the same color