I would expect a USB 3.0 memory stick to make full use of USB 2.0 in terms of read speed, but for write speed AFAIK they're all rubbish (one interesting fact is the lack of official manufacturers' stats wrt their performance*).
Kingston's DataTraveller Mini 3.0's datasheet reckons it can read at 70MB/sec, so therefore if connected to USB 2.0 it will go as fast as the controller would let it. I'm a bit dubious about that 70MB/sec figure personally, but even if we say the real figure is half that, it's still fast enough to be bottlenecked by USB 2.0. Usually memory stick write speeds are about 5MB/sec.
That memory stick model is one of the few types I came across on the Kingston website that mentions performance.
* - admittedly I've been looking at the low end first, and my interest was mainly in write speeds because I sell memory sticks for backup systems in a lot of low-capacity scenarios.
One other thing, if you want performance, get an external hard disk instead. I've yet to see a modern external HDD that doesn't beat the crap out of a memory stick in both read/write performance.
- edit - I've just had another look around, specifically at the high end of Kingston's selection, and they reckon that the DataTraveller R3.0 G2 can do 120MB/sec read and 45MB/sec write (apparently the 16GB can only do about 25MB/sec write though). A 16GB model is double the the price of the average 16GB stick, but I might give one a spin out of curiosity. Wrt OP's question, the figures in this paragraph all relate to USB 3.0, but based on these figures, the adapter should be fast enough so that the 2.0 controller is the performance bottleneck.