Most likely, no. It's not impossible, but improbable that this is actually happening.

While a lot of people have anecdotes they say confirm this it's the exact same kind of proof as people have of precognition. "I was JUST talking about her, and she called." "I was JUST thinking about him and then he called" and so on. It happens a lot because of our cognitive biases, our brains just aren't as perfect as they make us think they are.

Here's some other more likely explanations: You talk a lot about something, which means its on your mind for some reason. That reason might be that you've already seen a few ads for it, or that you've read about it online. It's also possible that since you talk about it in person you have mentioned it to someone online, or the person you talked to have mentioned it online or in some way shown interest.

These are all signals the major advertising networks (facebook, google) already take into account and track through cookies and so on. They are way less effort and way more accurate than some hypothetical "listen in on all your conversations tech", and thus far more likely to be the cause.

You're also forgetting about all the thousands of times you have been talking about this item before without ads showing up, and all the thousands of items you've talked about that have never led to any ads showing up.

But sure, it's possible they have constant surveillance on you. Not likely, not very believable, but it's possible. It would only work when the phone is not asleep though, which means when the screen is on and active. Anything else would cause massive, massive battery drain and likely huge data usage as well. (Well beyond what certain apps are already famous for)

In the end the only good answer is this: if you feel this is something a certain company might actually do then assume they are doing it and consider whether that changes your feelings about using the company's products.