Got my E367 dongle from 3 mobile today (decided to go in store), and just confirming that yes indeed, it works with the Edimax 3G 6200n with firmware v2.2 without issue. It correctly displays as a "huawei E367" on the modem status page.
According to the status page, I'm getting a 58% signal (in W6 area), which is already an improvement from what I had in the past, but I am *really* impressed about the speeds I'm getting now. With all the high buildings and interference in the area, I've generally been achieving around 2 Mbps tops. I'm now running double that and ping times have been reduced to about 80ms-ish (that's with the WiFi router in the middle). I have taken those "up to 40% faster speeds" ads with a large grain of salt, but in my case it really did make a difference
Oh, and these dongles also have a little plastic/rubber piece covering access to an external antenna connector (looks like a proprietary size to me - it's on the side near the SIM cover). So there's no need to hack your brand new device to boost the signal - just plug it in. Thumbs up!
And once again thanks to markthomas for being the guinea pig on trying it on the Edimax.