I guess it depends on what lighting you're using. Most coral-specific lights tend towards the bluer end of the spectrum (thinking 20K, actinics, etc) and omit some of the range that chlorophyll likes best. 6500k to 10k would probably be your best bet for growing veggies at the same time, though it might also spur an increase in algae.
Another thing to consider is possible salt spray/creep. Just be careful that your setup doesn't have the potential to get salt or saltwater into your growing media or you'll quickly find your plants starting to struggle.
Being in close proximity to your tank will likely raise the local humidity levels a bit (something that most herbs and veggies grown indoors struggle with because they tend to dry out in our homes), but the light spectrum and salt proximity might not be the best mix. You're talking about cheap plants though, so I'd say give it a shot and see how it goes. :)