As far as the legal prohibitions, check with your local township. There’s no national law, it’s all based on local safety codes. There are some places where it’s not a problem, but there are many where it is. So this is one of those things where the Internet can raise a question, but you need to check local authorities to get an answer.
Assuming that it is legal in your area, then the safety questions.
If you give us the brand and model number of your fireplace we can check the manual, but I would bet a virtual pizza it’s got an instruction that it should not be operated unattended. If I remember correctly, that warning is required for UL listing, for example. I know it is for space heaters, even the ones with programmable timers.
On to smartthings issues. You’ll see several reports in the forum Every month from people reporting their lights went on unexpectedly or the garage door opened unexpectedly. Or the siren goes off by itself. We usually call them “poltergeist” events in this community. 
They happen sometimes, and sometimes they happen because of events in the cloud that we just have no control over.
So speaking just for myself, I don’t put anything on smartthings that I would feel uncomfortable running unexpectedly for 24 hours unattended. But that’s just me. Everyone has to evaluate this situation for themselves. Just know that it might happen. For example, many of the people who have automated their fireplaces use relays which have internal timer shutoffs that aren’t in any way affected by smartthings working or not. That way even if one of the poltergeists strikes and SmartThings Turns on the fireplace when it shouldn’t, the relay will turn itself off again after a fixed period of time. So that sounds similar to what you’re proposing.
Again, speaking just for myself, I don’t typically try to convince anyone one way or another on projects like these. 
I do encourage them to be aware of the issues and to contact their own local township Before proceeding.
I wouldn’t skip that step. Fire safety is one of those issues where your mistake could kill me, because I’m in a wheelchair and if we’re neighbors, a fire at your house could reach me before help arrives. This basic issue of shared vulnerability is why fire safety codes are taken so seriously in most jurisdictions.
But I won’t say it’s never legal or safe to automate a fireplace. It depends on where you live and how you do it. So it’s just a project which requires a little more research than swapping out a light switch.