Yes. I have a combined smoke and CO detector in the garage.
I was worried it would trigger a lot with car work and brief engine runs and occasional light torch work on rusted car bolts (I do a lot of work in the rust belt). But that has not been a problem. I suspect the CO detector is more important since if someone ever runs the car without the door open that can be deadly (particularly if living space above). I can easily hear the alarm in the house. I think I only had a few work triggers in 10 years. But I do not do much torch work or welding inside. I tend to do stuff outside when I can if it generates a lot of fumes (heavy part cleaning, welding, painting if possible ...). It is best not to get those kind of fumes in the house regardless of the alarm level.
In terms of Li-Ion batteries: I strongly recommend storing and charging batteries in a metal cabinet with some buffer to combustibles. High capacity batteries do go bad and the heat generated in a failure can be stunning. I know one guy at work who had a yard tool (battery in tool?) catch fire in his garage and nearly burn down his whole house and off him and his wife. You can also put the chargers in a metal cabinet to leave when charging for added safety. But I would NOT leave batteries in a charger near anything combustible. The real danger is high capacity batteries ... and some yard tools have high capacity ones. I also wonder about the wisdom of people with solar panels attaching battery packs to the sides of their homes for night use. That seems like asking for trouble. Perhaps if such is in something a bit away from the house in the yard, that could be ok. But on or in the house .... yikes, no. I have similar worries on electric and hybrid cars. Yes, I realize gasoline burns too if one is careless. But battery packs can go up *without* doing anything dumb and have limited life. If you have a lot of them, that is a lot of risk. I presume electric cars and home banks have some degree of isolation and thermal protection built in ... but I am skeptical if that is enough in potential failure modes. I do not think high battery capacity tools have such protections.
I would add that some remote start cars seem like a bad bad idea for garage storage. It is like asking to have a problem if they do not have some sort of confined space interlock (how would THAT work?). If you might ever own something like that I would for sure have a CO detector with a loud alarm in the garage. Press the wrong key button and get asphyxiated seems like a dumb thing to market.