No, I don't think you can cover the roots with more soil. Palm roots are naturally close to the soil line (and often above it). Being planted too deep leads to root rot.

Fortunately, palm root balls are rather compact, so, you should be able to dig a few feet away. Pick underplants that have a wide perspective and you'll still get the look you're going for.

1. You will kill the Areca palm by covering the roots.
2. Planting anything under it is a bad idea, as stuff falls from the palm on a regular basis - dead fronds, dead bloom spikes.
3. You will create a maintenance nightmare for yourself by planting stuff under it.
4. Anything you plant will not do well as the palm will suck all the water and fertilizer from the soil.

Mulch the area and move on.