They might survive, best chance is to keep it in a pot water; sometimes they sprout back from the roots.

But they are super easy to grow from seed, I don't know why you think it is hard. And in the right conditions (adequate sun, moisture), you can have a blooming one in just 3 years.

I've tried since I was a kid to grow a buckeye from seed. 98% of the time they did not germinate. The slim couple that did died :( I guess it can be considered my botanical unicorn lol

You need to come up here to NJ and kidnap a couple of the squirrels in my yard, because all the buckeyes they bury germinate and grow - in the compost bin, in the middle of the driveway, in the hedge, in the lawn...

Yes, you have to protect them from squirrels. I gather all mine that I can each year, make up 1 gallon containers with average soil, put a buckeye in the top 1 inch of soil and then put them safe place outdoors that can get watered over the winter. By mid-winter (January), you can see them coming up.

But you have to keep the squirrels away. Screen or hardware cloth works fine.

Come spring, I have a bunch of plants to donate to the local native plant sale.

Cool, moist stratification is the key - if you've carried that buckeye around in your pocket all winter - or had 'em sitting in a bucket somewhere drying out - and then plant 'em in spring, you're not gonna get any growth.

Taproot? It's not a magical thing. Yes, they do provide anchorage, but mainly, they're a 'reserve energy storage vessel' storing and providing energy to push growth at the next leaf-out. Sure, when I'm digging a taprooted species for transplanting, I try to preserve as much taproot as is practical, but If I cut it shorter than I like, I don't consider it to be a death sentence for the tree.