Not out of the box, and anyone telling you otherwise hasn't tiled the file. Ask for “seamless repeating pattern” and Nano Banana gives you a beautiful, evenly distributed, all-over design — but the left edge doesn't mathematically continue into the right edge, so tiling it produces a visible seam every tile width. That's true of every current general-purpose image model; seamlessness is a geometric constraint, not a style, and these models generate pixels rather than solving constraints.
The fix takes about two minutes and is completely reliable. Open the tile in any editor with an offset filter (Photoshop's Offset, GIMP's Offset, Affinity's equivalent), shift it by half its width and half its height so the former edges now meet in the middle, then heal or clone over the visible cross-shaped seam using the pattern's own motifs. Offset back and the tile repeats perfectly. Prompting for “an evenly distributed all-over pattern with motifs of similar scale and no large empty areas”, as every prompt here does, makes that cleanup trivial — a dense, even design has no awkward gaps to patch.