The bit depth (read: word length) of an audio file defines its dynamic range. CDs are 16 bit, which is 96dB of dynamic range, minus a little dithering at the bottom end. 24 bit would get you 144dB, which is unusable in any audio system. Even 96dB of dynamic range is barely achievable with extremely low noise electronics in very well sound proofed rooms. This is almost certainly a moot point given that most modern recordings have about an 8dB crest (peak to average) factor.
Increasing the sample rate a little is probably a good step, but again modern AD/DA converters deal with this quite well. Properly reconstructed (read: oversampled) there should be no difference to our ears (which can barely hear past 18kHz) from an increased sample rate, and there is a much greater burden on the processing hardware. File size will also go up.
The real issue is that neither of these specifications defines audio quality. iTunes Plus did increase audio quality by doubling the bitrate of the AAC codec. I cannot hear the difference between CD and 256AAC. If I can't hear it it's unlikely than almost anyone can.

The best way to convince a boss of anything is to show them the numbers. If you can put something in a cost benefit analysis (CBA) and show how much work you do (A list), they'll be hard pressed to argue. Also, you can talk to them about what happens when you take a vacation, which you want to do because you're overloaded. However, actually running out and doing it, as was previously suggested, might just get you fired. It depends on the place you work, but with government contracts on the line...
Finally, I'd like to suggest that you re-evaluate IT's (Information Technology) place in your organization. An information system (IS) is, essentially, an integrated set of services and software that makes things easier for the company (IE a transaction processing system, or decision support system). The IT department is usually in charge of maintaining the IS's in a corporate environment and ensuring that they interoperate well with the actual hardware within the company. Having the ability to review software during the selection process to ensure that it integrates well into your environment is something that should be mandatory. Also, and IT department is not *just* about connectivity. It's about integration and support of all information systems from that database programmer in accounting all the way to the boss's hotsync software.
Good luck,
-D

Yeah, right, put a link to a 4.9MB file on the front page of slashdot. Gooood idea.

Like shooting fish in a barrel.