No expert here, but I would think if the runners put down roots, they should get nutrients that way.

Also many plants can absorb nutrients through the pores of their leaves, hence foliar feeding.

Plants get nutrients from wherever they have roots. Most nutrients come from the main root ball, but they can get nutrients from adventitious roots on other stems touching the ground as well.

Watermelons are known to send out adventitious roots along their stems, so yes, they can get nutrients from those.

Thank you all. I didn't notice any established rooting on the runners, so to speak. Next yea, when I try again with new knowledge, I'll see what happens ! Thanks again. Geezerman

Clay, you might want to "pin" a few runners to the ground to make sure they maintain contact. I just use strong floral wire to make u-pins to pin things to the ground or soil, or for larger things, like rose stems, I use a rock or brick. For roses or larger things, you need to scrape the bottom of the limb you're pinning, then just stick a rock on top, and VOILA! Next year, you can cut it off and have another plant. I just pinned strawberry runners into the hanging basket the original plant was in so I can have more strawberries next year.

Thank you.. I'll be trying that. Geezerman