OK, so I tried this pretty much as I described and was generally pleased with the result. I used flour but no "binding agent". First attempt was with no baking - just dropping the formed raw tater tots in 350-degree oil on recommendation from my "sous chef". It was a disaster. Everything fell apart and we ended up with fried, shredded potatoes that tasted pretty good.
Here are the uncooked shredded, dewatered, S&P'ed, with onion and parsley potatoes formed into tot-diameter rolls.
Next, I baked the "logs" for about thirty minutes, which set them well enough that they stayed together, so I could cut them into tot-length pieces for the deep fry. The results, while not perfectly shaped like the Ore-Ida version, were pretty good.
I probably wouldn't do this again, opting instead for the store-bought version to satisfy the tot fix. Looking forward to trying Chef Tavis' version at the NABC/Louvino pop-up.