I repotted an areca palm, and unfortunately set it too high in the pot, so the top of the stems, which meet the roots, are slightly exposed at the top.
What happens if I leave it as-is? Will the plant adapt?
What happens if I leave it as-is?
Your roots may get infected, that would ruin health of your plant. Also, insects\ants can start feeding on roots.
Will the plant adapt?
No. At least not this instance (your tree). You would be knowing that adapting to change of environment is ongoing process, may be if all the palm trees are treated like this, may be they start adapting this thing, and built the capability to withstand the open roots in their future generations.
Bottom line: Its better you re-pot it again!
No, as Jaczjill says, you need to pot it again, this time making sure it's at the same level it was before. Those roots are used to being under the soil, and have a job to do - being exposed means they'll dry out at the very least.
Just take the time to re-pot it, however beware over-working the palm's especially sensitive root ball. Palm tree roots are especially sensitive (to direct fertilization, as well as transplant shock).