Is there any benefit to plugging a USB 2.0 device into a USB 3.0 port?

Since your USB is optimized for USB 2.0, using a 3.0 will see no improvement because it simply cannot operate at 3.0 speeds.

USB 2.0 has a maximum speed of 60 MB/s USB 3.0 has a maximum speed of 625MB/sec

From Wikipedia's Article on the Universal Serial Bus:

Typical hi-speed USB hard drives can be written to at rates around 25–30 MB/s, and read from at rates of 30–42 MB/s, according to routine testing done by CNet.[62] This is 70% of the total bandwidth available.

Based on this, you can see that USB 2.0 devices just are not capable of the speeds 3.0 has to offer.

TL;DR version: You will see no benefits

One advantage could be that USB 3.0 can supply more power than USB 2.0.

I have some doubt whether an USB 2.0 device could use that power, as it would be designed for a USB 2.0 port. On the other hand many USB 2.0 devices exceed the specified power and get away with it (mostly external disks when they start up).

Actually, yes, it will be faster by a small margin. You will only see gain if the device in question can dish out a higher bandwidth over another interface like ExpressCard or PCIe. for instance a modern 7200 hard drive in a external enclosure could more than saturate the USB 2.0 port. If the enclosure is a USB 2.0 device, it will be operate with more of its bandwidth when plugged into a USB 3.0 hub, but not nearly as much as if it was a USB 3.0 to USB 3.0 device to hub link (with a USB 3.0 cable).

At least on my laptop, USB 2.0 external 500 GB on USB 2.0 gives me about 19–23 MB/s and up to 25–32 MB/s when connected to a USB 3.0 express card. So I am getting both a higher minimum speed and ceiling when the same USB 2.0 device is on the USB 3.0 hub. I think the controller is probably more efficient on USB 3.0. When I plugin a USB 3.0 thumb drive on the same ExpressCard USB 3.0 hub though, I get up to 122 MB/s.

So short answer; yes, a small increase, but not nearly as fast as native USB 3.0 links.