Unheard of, no. Likely? That's a different story. Other than the occasional discount store closeout, which is likely to be in an odd size or style (or both), I doubt you will find anything decently made and fully canvassed (I'm sure some online MTM will make you a terrible but fully canvassed suit for peanuts if you so desire) for under $700.
Also, I hate to be the bearer of bad news, but most of the suits you identified above are not fully canvassed, but half-canvassed. The BB Golden Fleece and HF Mahogany lines are indeed fully canvassed, but you're talking about $1,500+ suits. The link you posted to HF is for a tan suit, and even that is $800. That just illustrates my point that you can occasionally find something "fully canvassed" for $700 or less ($800 in this case), but it's doubtful that you will find anything in a staple color/style from these lines at modest prices.
In any case, I was more trying to point out that there is nothing wrong with a half-canvassed suit, and $700 is not an unreasonable price to pay for one, at full retail or on sale. BB 1818 suits are half-canvassed, and are excellent value at BB's regular sales (when they are routinely available for about $700).