If it's a treatment that is required for the patient to survive it will generally be available & free. E.g. getting cancer treatments here will be free & almost certainly expensive in the US (even with insurance they will find something the insurance doesn't cover, and/or will charge you for stuff like ambulance rides).

There may be some rare exceptions where you'd be able to pay a lot of money in the US for some experimental treatment not yet available in the public EU system but this is the exception not the rule. What you possibly won't get for free are non-critical treatments.

I will give one declaimer though that I live in Germany & the healthcare system is not in the same quality/extensiveness throughout the EU (the German system is among the best).