This question is almost too broad or open-ended. Even so, I want to put in my two cents.
This question appears to rely on the assumption that receiving bitcoin from an exchange will magically provide history-free coins that are no longer linkable to one's identity. There are some problems with that.
A. The coins will always have a history. Maybe you'll get coins that were recently mined and have no real history. Or maybe you'll get coins that are later linked to a crime. Whether dirty or clean, the coins always have a history. Assuming you manage to retain the anonymity or privacy you seek, you still may end up with tainted coins.
B. More obvious, but it's worth pointing out that it's not like you can transfer bitcoin from the exchange to your existing wallet. If you do, then you may end up spending the "history-free" coins along with existing coins, thus linking them all together. This means you're stuck managing an additional wallet. Maybe it's not a big deal. But it's jumping through unnecessary hoops, unless simply have to spend bitcoin. And even in that case, you can just use xmr.to.
And then two more things:
"High likelihood" is a subjective term. If you're suspected of breaking a law or acting unethically, then the scenario you described could easily rise to the level of "high likelihood."
Just by trying to leverage one coin's privacy features to manufacture privacy in another coin, it makes it look like you're going out of your way to hide something, which makes you suspicious. It's like if you use a coin mixer, except in your scenario there is at least some doubt.
The bottom line is that you're probably best off by remaining in the Monero ecosystem, where you get privacy by default.