Sure, but it appears there is manufacturer's required clearance to each side of the cooktop. My gas cooktop required 3" side clearance to combustable materials.

Some ranges do require up to 12" for combustible surfaces on each side, many seem to require 6". If you have at least 9" that would also meet the minimum side set down recommendations as well. I would make sure the underlying surface behind the back of the top is also noncombustible including down behind the back of the cooktop which is also required by some. (Also some require use of their supplied high back guard for certain installations.

Following the specs is very important because even if it passes inspection if your kitchen did catch fire, your homeowner's insurance could be voided if you do not follow the specs.

Pictures? No you shouldn't tile it. Is it going to be that close?

Mark_Rachel, no, it’s not, but all I have is a mock-up drawing intended to give me a general idea of what a heath-style vent would look like that makes the space look really close. A couple commenters can’t get past the drawing, and are obnoxious driving their point across, so I decided to post the question without the drawing since it seemed to distract from my question.

Skip the tile. It will only build the side out & make it even closer. (I typed this before & it disappeared...)

Tile applied to wood won't have the most permanent of bonds. Wood expands and contracts. That will loosen the tile over time .

I had to hunt down the other post. It's not a good design. But that is easy to change in the drawings phase!

live_wire_oak, thank you so much for a response that actually addresses my question. You are absolutely right about wood expanding and contracting. It seems obvious, but I didn't think about it until I read your comment. And, thank you for understanding that this is the drawing phase. I told my designer that I'm going to be the problem child in the design phase. Anxiety level: through the roof - sigh ...