Can I leave my swaybar upsidedown?

Depends, do you want it to work correctly? Or just hang there as an ornamental piece of steel?

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Are you sure that it's a rear sway bar? All the sway bars I've seen have angled arms coming out of the ends that are linked to each side of the suspension. Additionally, there are bushings that allow the sway bar to rotate to impart torsional force to resist the motion of the suspension travel.

Your picture shows no end links or bushings.

Here's a picture of one side of a Gen 3 rear sway bar with bushing under the strap clamp on the rear beam and end link connected to the rear suspension.

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The ones in Gen 1 and Gen 2 Prius rears just sit there in the channel of the suspension beam and increase its torsional rigidity, which is pretty much what sway bars do anyway, so it's fairly named.

The ones in front have longer arms on the ends and link up to the MacPherson struts, in a clever way that actively counteracts lean while cornering.

Because the rear one just kind of stiffens that beam, it is probably doing that to some extent even though it is upside down. In other words, it's already more than an ornamental piece of steel.

On the other hand, to get the intended degree of stiffening under the intended conditions, you may want to put it in the right way.

 

Here's a Repair Manual excerpt. Quick glance: your's in the right location, between the flanges of rear solid axle, but connected to wrong flange??