It depends on how it'll be lit. If it's low-poly and needs to be lit through basic vertex lights you'll want to probably connect those pieces together and avoid long strips of geometry.
'Floating geometry' generally uses less triangles but it will cause some overdraw at the point where the 'floating' geo sits over the mesh. It's a trade off between tri count and texture but I think it's mostly always better to use less triangles.
Floating geo is totally fine if it looks ok in-engine and lit. It really depends on what kind of lights you'll be using in the scene if it's not going to have a lightmap baked onto it and so on.
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