Is it normal for the flat deck on a tub to dip in the middle?

Steel tubs get stamped in one press stroke and that wide flat deck is the hardest part to keep flat, so a little waviness out of the box is normal. But a level that see-saws and only touches at the ends is more than waviness, that's an actual bow in the panel. I've set a couple of these steel tubs and can tell you how the mortar question works out. The bed supports the bottom so the tub doesn't flex and creak when someone stands in it, but it doesn't straighten anything. The tub keeps whatever shape it came out of the box with. And you really don't want to try pulling the middle up flat while the mortar cures. The porcelain coating on steel doesn't like being flexed like that, and you can end up with hairline cracks in the finish that turn into rust spots a couple years down the road.

As for water pooling, the deck is supposed to slope inward toward the tub so splash runs back in. A shallow dip in the middle of that slope will usually still drain. Easiest way to check is the water test. Pour a cup of water on the deck near the middle and watch where it goes. If it trickles toward the tub you're probably fine. If it sits in a puddle the size of a saucer, that's what you'll see after every shower, and standing water on enamel eventually etches and dulls it.

With a bow you can see by sighting down the edge, I'd take it back. Scribing tile to a bowed flange means a gappy or wavy line where the tub meets the wall, and once it's bedded in mortar you're stuck with it. If the store allows it, throw your level on the next one before you leave, or at least check it in the driveway before it goes downstairs. Sorting through a few boxes beats redoing this in a guest bath.

Before you haul it back, check it on a dead flat surface. Mine looked bowed in the bathroom too, turned out the subfloor near the drain had a dip and the tub was just following it. Laid it on the garage floor and the level barely moved. If it still rocks on flat concrete, yeah, swap it. Also run your hand under the deck while someone presses down on top, if you feel it oil-canning that's a diffrent problem than a gentle bow.

Swapped one of these at the same stage of a remodel a while back and the store didn't even blink at it. Worth asking about thier return window before you mortar anything, some places get picky once you've handled it a bunch. Also check the new one in all four directions with the level, not just across the deck. Mine looked fine one way and had a twist the other way that I caught on the second pass. One more thing, don't stack anything heavy on the deck while it's sitting around waiting to get set, that's an easy way to make a good tub go bad.

Update: took the garage floor test from the second reply and it changed everything. Tub sat flat on the concrete, level barely moved. Turns out my subfloor has a dip near the drain and the tub was just following it. Shimming and leveling the floor before the mortar bed now. Keeping the tub, no return needed.