Tent - yes
I will always sleep in a tent in the desert.
I had a buddy that got bit by a brown recluse on a trip on the Green above Moab. He did not think much of the bite not knowing what bit him, until he was past the confluence and committed to running Cataract canyon. Oh boy, huge mistake, the bite swelled up like a golf ball, he was delusional, had high fevers, and he had to finish a challenging run in an open canoe.
When got off the water he rushed home and Boulder community keep him in the hospital for a couple days. He was sick with fevers for 6 weeks after and has a nice hole/scare from the spider's poison that killed his flesh. His bite was not even considered bad by Brown Recluse standards.
I also recommend a tent that you can close tight, if winds come up and you are camping in sand.