Not so different than in the States, e.g., 1) Will all US health care accept all forms of health insurance? 2) Will all US health insurers
pay for all sorts of care at all sorts of US healh care providers? Nope x 2.
Which type of care? True emergency versus regular illness? Regarding your 2 very broad questions, the answers depends on a LOT of things x 2. Reasonable responses include maybe, maybe not, sometimes, & nope.
Depending on the form of care, sometimes the cost is low enough you just pay. On the other hand, some foreign hospitals require payment up front. Then, a US-insured patient fends for themselves to potentially be reimbursed by a US insurer.
Making specific plans for foreign travel
@temery?