I'm not going to be able to give you a definitive answer because I'm not familiar with the actual style and can't confirm or deny that Coach might have made a style of desert boots.
But based on my familiarity with Coach (in general) and its shoes, boots, sandals and sneakers, I feel comfortable in making some comments on why I think the boots are fake.
1. Style - although I'd never go so far as to say that they wouldn't have made a certain style of item (because we've all seen fugly items that have us saying "what were they thinking?") the boots just don't look even like one of those types of items.
2. Sole - though many of Coach's items have rubber soles, more often than not, the treading is a signature pattern rather than generic ribbed patterns. (I did find one boot style - Cantina - which does have a ribbed sole, but the Coach logo is the readily identifiable script pattern and the sides of the soles also have the Coach script logo.) And where there's a "COACH" name, it's either a lozenge logo or script. I don't believe that Coach would use a font such as is on your boots.
3. Insole label - usually on leather insoles, there's an embossed lozenge logo in Coach's familiar font. On items with a sewn on label, the label (in my experience) has a lozenge logo, as seen below:
4. Size and style information - font differs and information appears to be lacking, as compared to this:
I don't know for sure the answer to your question but based on what I do know, I don't think they're authentic.
Can they be returned?