Well, if you want 100% plug and play, then yeah, that converter should work. It's totally unnecessary in terms of function, but it'll work. You could use it on other consoles, too. My only concern would be that the conversion appears to be digital. It may lag. It's also almost guaranteed to use 4:2:2, which results in a (normally unnoticed) blurring of the color (but not brightness) information.
Beware the cost of Uniarcade. Paying them is quite a hassle (you can either wire them money or use Western Union - neither is free), and shipping is high since it's coming from China. Decent folks otherwise, though. Quality is highly variable on some products. They also messed up one of my orders and would not correct it, leaving me with about $100 worth of useless merchandise.