Yes, you will need a modifier when reporting codes G0402 & G0403 together. While there is no CCI edit in place for the code pair, Medicare Claims Processing Manual instructions state that modifier 25 should be appended to an evaluation & management visit when performed with another significant procedure. In this instance, the G0402 would be considered the E&M.
G0403 is the global service, so the provider would need to have completed the ECG test and then provided the interpretation and report. If another place provided the ECG, they would submit G0404. The physician providing the interpretation & report would submit G0405.
For FQHC/RHC claims requirements, guidance is found within Publication 100-04 Medicare Claims Processing Manual, Chapter 9, Subsection 70.6 Initial Preventive Physical Examination (IPPE). I've copied & pasted the instructions below because there are some particular nuances for your scenario, e.g. the professional component is part of the AIR reimbursement. Due to this, you may need to submit G0404 on the claim.
70.6 - Initial Preventive Physical Examination (IPPE)
(Rev. 3434, Issued: 12-31-15, Effective: 03-31-16, Implementation: 03-31-16)
"FQHCs and RHCs billing under the AIR system Medicare provides for coverage for one IPPE for new beneficiaries only, subject to certain eligibility and other limitations.
Payment for the professional services will be made under the AIR. However, RHCs/FQHCs can receive a separate payment for an encounter in addition to the payment for the IPPE when they are performed on the same day.
When IPPE is provided in an RHC or FQHC, the professional portion of the service is billed on TOBs 71X and 77X, respectively, and the appropriate site of service revenue code in the 052X revenue code series, and must include HCPCS code G0402. Additional information on IPPE can be found in Chapter 18, section 80 of Pub. 100-04.
EKGs
The professional component is included in the AIR or FQHC PPS and is not separately billable.
The technical component of an EKG performed at a RHC/FQHC billed to Medicare on professional claims (Form CMS-1500 or 837P) under the practitioner’s ID following instructions for submitting practitioner claims for independent/freestanding clinics. Practitioners at provider-based clinics bill the applicable TOB to the A/B MAC using the base provider’s ID.
FQHCs billing under the PPS:
IPPE is qualifying visits when billed under G0468, for additional information on the payment specific codes and qualifying visits, please refer to section 60.2 of this manual. Under the FQHC PPS, IPPE does not qualify for a separate payment when billed on the same day with another encounter/visit."