Some policies will not cover you if you do not have health insurance here in the US, though this is very rare and only the companies HTH Worldwide and GeoBlue will make this mandatory with all their policies, though it's worth noting that most multi-trip medical policies will also require you to have primary insurance.
If a policy requires this, they will always list the requirement in the 'Additional Notes' section of an insurance quote. This does not mean that your primary provider has to provide coverage internationally, but you must have health insurance in effect in the US in order to be covered by any policy with this requirement. For the purpose of meeting this requirement most any provider will work except for Medicaid. This will always be specified in the policy certificate.
Also, in some cases, having primary coverage will improve the benefit provided for a recurrence of an existing condition.