Granted, it officially would not be beer (dunno what it would be called), but as a cereal grain that is maltable and grindable, it seems that it should also be pretty brewable. I'd be interested in making something like that just to try it... but googling has turned up nothing on it, so I'm curious as to why that is.
A similar question was asked here on the BN forum. It all boils down (no pun intended) to whether the wheat malt will have enough diastatic power to convert itself.
The answer to that is a little confusing to me so far. The charts at the Home Brewing Wiki here give diastatic power as percentages, but other references I've found use Lintner or Windisch-Kolbach units. Below °L is "degrees Lintner", not Lovibond.
According to most of the sources, a malt needs a diastatic power of approximately 35 °L or 106.5 °WK to be considered “self converting”. Taking a look at Breiss' wheat malts, they claim 190-200 °L for their "high enzyme" wheat malts, which is higher than the 6-row!
So find out the diastatic power of the particular malted wheat you want to use. If it's > 35 °L, you should be in business for some mashing action.
1) It would be beer. Beer is an alcoholic beverage made from grain, it doesn't have to be made from barley.
2) The most important thing to remember about wheat is that it has no husk. No husk = no filter bed for your grain when you lauter. No filter = stuck mash. It is possible to lauter an all-wheat mash, but it takes a very long time and is tricky. This is basically why no one does it.
Edit: A book that talks about all-wheat brewing is The Brewer's Apprentice. In it, a German wheat-beer brewer talks about the percentages modern breweries use, and how older breweries would make beers from 100% wheat. He's pretty dismissive of the practice, saying "They must have had a lot of time to lauter." (that quote's from memory, so I'm paraphrasing).
Yes, you can brew a beer from 100% malted wheat. It will absolutely convert. The Weyermann pale malted wheat is 200+ °WK (Windisch-Kolbach units, which converts to ~ 62° Lintner).
That said, Weyermann recommends...
"Recommended Quantities: Up to 80% in Bavarian-style Weizenbiers, up to 50% in North American pub wheat ales, up to 7% in Altbier and Kölsch"
You will need a lot of rice hulls if you go with 100% wheat to help with lautering, but I'd go ahead and try it if the fancy takes you.
If you do it, I'd be interested in the results.
I'm guessing from your title you're interested in using non-malted wheat to contrast with using malted wheat? If so, then yes, that's often done in brewing.
For example, a Belgian Wit typically contains around 40-50% flaked unmalted wheat. And some English beers use torrefied (puffed) unmalted wheat as ca. 10% of the grain bill to aid in head retention and add.
Looking further afield from wheat, some of the big brewers use plain rice rather than malt to lighten the body since rice is almost completely fermentable and produces little color or body, just alcohol. It's also a lot cheaper than malted grain so it lightens their check book too.
All of these come under the heading "cereal adjuncts". Is it possible to make a beer with just unmalted cereals? Fortunately not, or it wouldn't be beer as we know it, more like rice wine. (And for that, you would need to add amylolytic enzymes to break down the starch.)
One of the main side-affects of malting grain is that additional enzymes are created in the grain. When the malt is mashed, the amylolytic enzymes break down the starch into mostly fermentable sugars, and some non-fermentable sugars. Malted barley contains plenty of these enzymes, enough to convert it's own starch plus other starches added to the mash, such as cereal adjuncts. But, there is a limit - with the best enzymatic malts, you can use about 40% grain and 60% adjuncts and still get full conversion of the starch, but that's as far as it will go. Trying to use even more cereals will leave starch in the beer, or require the addition of more enzymes (as is done when making rice wine.)