NOOOOOO
It is NOT safe. I cannot stress how dangerous that is!
The computer is always drawing on that battery if it is on, and if it is smoking then it means whatever coatings and insulators inside the battery have given away. Lithium Ion batteries contain so much energy. If you google lithium ion battery explosions you will see how much energy is contained inside those batteries.
If it is smoking then it means that something has caused a battery failure, and the battery is shorting internally. If it's stopped, it most certainty doesn't mean it won't happen again, it's only a matter of time before it does, and if that battery fully ignites, it could burn the room down. I would strongly recommend that you remove that battery and get rid of it as soon as possible.
It is no longer safe to use. The insulators inside have burned away and it is extremely likely that a short will occur again. Please, for your safety, remove that battery. I know there are warning signs everywhere nowdays, like on a hammer it tells you to wear 6 different protective things, but this is a serious danger. Lithium Ion batteries, when they pack in, can literally burn houses down.
Please, replace that battery.
On a second note, a replacement battery should last a lot longer than half a year. Knowing iFixit's standards, I doubt its a quality issue. If there was a reason to replace the battery in the first place, and something fried the old battery, and you put a new one in and within half a year its fried to smoking point, it points that there is a problem with the computer. Either something is drawing way too much power, like something is busted on the motherboard and is shorting power, or there is some little piece of metal that is shorting a contact. Usually its when batteries get shorted that they fail in style(going up in smoke counts as failing in style). So I would recommend that you get your computer checked out.
Let me know if this answers your question!
Cheers,
Falcon