it probably would be better to cook em down a bit
as compost. i could be wrong but if they are in their present state ,their not gonna offer much to the plants. next year maybe,but i dont think they would offer much in their present state other then fluffing the soil a bit.ive grown watermelons but ive never grown good watermelons!!
kinda would like to see what it takes to grow a good watermelon.

when i said cook em down a bit,i meant to compost em. shred em if you can,mix em in a big pile(3 foot by 3 foot) with green stuff...grass clippings,vegetable waste from the kitchen,coffee grounds,tea bags,tater peels, left over fruit and vegetables. water the pile well as you make it and let it sit .every week or so turn it over to expose the inner part to air. it should start to get warm and if its really going well it will actually get hot!
eventually,it will break down to a dark crumbly substance known as compost. mixing that with you garden soil will greatly enhance it. but it does take time. starting now,your not likely to have any before your melons are well on their way.
you can place it around and dig it in around exsisting plants and it will do some good but its real beauty is that it enhances your soil
and makes it much more appealing for future plantings. if you have the room for such an endeavor, i highly recomend it. otherwise you can buy compost and mix it in before you start your garden. its just so cool to take what we would normally have to dispose of and come up
with a real use for it. i have a pile cooking right now and its almost ready. smells reall earthy like and i didnt have to pay a waste hauler to take the thirty or so bags of leaves off my hands last fall. once i shreeded them with the lawn mower i had a pile about 4'x 4' and started adding green waste as i generated it over the winter. first couple mowings worth of grass clippings went in also. checked it the other day and its getting hot right now.