You can put whatever tyres you like on any bike as long as they fit - just dont expect it to handle the same if they're not recommended..
The problem with knobblies on any bike is performance on roads (braking, accelerating, cornering) and even more so on wet roads. Wear speeds up too and also knobs can fling off at high speed.
On the road it only gets worse with a sports bike which you can assume is more powerful than others.
Given those limitations you then cant ride your Fazer like normal, but as long as you remember that, you can have a whole lot more of fun on dirt.
I was fitting 17 trail tyres to a Suzuki GS (for a long trip) but have since decided to go up to 19" (so 3 x TW 302s for sale if you want and if they fit a Fazer).
More dirt oriented than TW302, but also faster wearing are something like Conti TKC 80s. The key with them is a low profile knob which squirms less under breaking and acceleration and so makes them run cooler and behave more predictably on the road. I got 5000 miles out of a rear down to Morocco and back (on a Tenere 660). TKCs are commonly fitted to GS BMs which I imagine are heavier and more powerful than a Fazer.
Try TKCs or trail tyres, but unless you have a dirt road trip in mind you may find the novelty wears off as you won't be able to ride a Fazer like normal.
There's a great Australian dvd, Up Top Down Under - a guy rides a GSX1000 up to Cape York, QLD (sandy) with knobblies.
Full knobblies make a real difference in sand, no matter what bike you're on. They are actually a lot safer. You just got to slow down on the road and in the rain.
I would not bother changing wheels unless you go all the way with suspension too.