Can the long curved piece go on the opposite side of the desk top so it on the left of the standing person, rather than the right?

I don't believe so, mostly based on the fact that there is another item that is sold as the "Left Side." Newegg Item #9SIAEVHEET7028

Questions & Answers: Eureka Ergonomic® L Shaped Electric Standing Desk 61", Electric Height Adjustable Stand Up Desk for Home Office Workstation, Black, Right Side

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Eureka Ergonomic® L Shaped Electric Standing Desk 61", Electric Height Adjustable Stand Up Desk for Home Office Workstation, Black, Right Side

Electric Height Adjustable: Equipped with dual motors and 4 memory buttons to easily customize the height of the desk from 29.9" up to 48.4".
Rock-solid Legs: The two heavy-duty carbon-steel legs can support up to 330 lbs (150 kg). Have your entire setup on your desk and game with confidence.
L Shaped Design & Ample Leg Room: L shaped desktop design lets you make the most of your corner space. The open dual-leg design is free of cross bars so you can make use of the entire space under the desk.
Large Desktop: Fit all your gear thanks to the 61" x 43.7" L shaped desk surface. Fit up to three monitors and all your peripherals with space to spare.

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