There was a jot of miscellaneous "junk" hung on the Hawk pylons over the years, a great deal of which was NEVER going to be practical.
Sea Eagle simply didn't fit - as DZ says the ground clearance was negligible, to the extent it was all-but impossible to load the damn thing onto the pylon (since the missile has to have clearance with the pylon in order to get under the pylon on some kind of loading mechanism). I believe one genius suggested loading it while the A/C was on jacks.
In addition, Sea Eagle has/had a minimum speed for release, to give the engine a chance to light up. I don't think Hawk could achieve that speed in level flight with it attached.
Skyflash was another "everything BAE must carry BAE weapons" marketing idea, and just as insane. Speed was just one of the issues.
But the stupidest stores option ever presented for a Hawk was a Kingston/Dunsfold special: In 1983, some clever person decided that carrying Stingray - yes, an anti-submarine torpedo - on the OB pylon was a good idea, and trial fits were carried out. There's a picture of it in the old Ian Allan/Arthur Reed book on the aircraft which never failed to amuse.
We were convinced that there was an Airfix model of the aircraft somewhere in marketing, and one of those boxes of random spare weapons, and every so often someone would glue a randomly selected weapon on their model, and decide it was a good idea.