IANAL, but cases involving that have been in the news a lot.

* Not being in the USA won't stop people from sending you bogus DMCA notices. Some places will honor them even if they don't necessarily have to.

* They can still sue. I remember one spam blocklist that got sued, in spite of being in the UK. But they had some volunteer or something (?) in the USA... allegedly. The judge entered a default judgment against them (nobody showed up) and they actually ended up hiring a lawyer in the end.

* Unless you really do have US assets, they probably can't do much, but that doesn't mean they won't try.

Different countries have different laws regarding safe harbors for secondary copyright liability. But if you're operating overseas, it would be hard to pin you down with this DMCA issue unless you have employees, an office, etc. in the US.