I'm no hearth specialist, but I did quite a bit of research in this area, after purchasing my home. You're not suppose to run the log lighter continuously. It's to be used short term. Even replacing the log lighter with a gas burner and logset may not be approved by the fireplace manufacturer...which is what I'm dealing with. My Fireplace box is only approved for burning wood and it may contain a log lighter.
Well, previous owner put in a full burner and ceramic logs. During my research, I came to find out that many gas burners don't create as much heat as a wood fire. Therefore, you have a lower upward velocity of air/smoke. This can lead to carbon monoxide leakage, through the glass doors.
Also, a gas fireplace may require a different flue size than a wood fireplace, to properly evacuate the carbon monoxide and smoke. Finally, my neighbor is a chimney sweep. he told me our Fireplace box is a low-clearance box and cautioned me about running the gas burner for longer than an hour at a time. According to him, since a wood fire creates more upward air velocity, the heat is able to escape faster than the heat generated by the gas burner. He says as a result, in a low-clearance box, the wood framing around the firebox can dry out and even char, to the point that it's a real fire hazard.
In your firebox, there should be a nameplate that includes things like date of manufacture, manufacturer's name, model number, serial number, and what uses it is approved for. If you deviate and say, run a gas burner in a wood-only box, and your house catches fire, you may have difficulty getting your insurance company to cover the repairs.
Since neither I, nor your Realtor, nor your plumber are hearth specialists, I recommend talking to one, before moving forward. For a small fee, they should be able to come out and give you the information you need to stay safe.
