Heat is definitely a factor in viability. Some species more than others: https://duckduckgo.com/?t=ffsb&q=seed+viability+heat&ia=web https://www.researchgate.net/publication/261617200_The_Effect_of_Temperature_on_the_Viability_Of_Weed_Seeds_in_Compost
Looks like the only way you'll find out is to try them and see.
I also think it is not a plantain.
I would mow the lawn regularly. As you see, the weed is tall, leaves exit the steam from a relatively high position. I would expect that such weeds will not survive if you cut often their leaves. The worst weeds are the the weeds which make a lot of stolons, ant they run lower on grass.
So mow your lawn regularly (maybe ...
That looks more like violets than plantain (too high to be plantain, which is about a half-inch tall rosette at this point in the year, assuming that you're in the Northern Hemisphere). The first photo also shows something with a fern-like leaf (Queen Anne's Lace maybe?). The grass itself looks old enough to walk on, so if you're careful you can try to ...
I have started collecting my avocado pits. I'm not sure how long they keep, just don't let it dry out! They're a bit involved for growing from seed but here's a link describing the process: