How could applying for Medicaid impact my pending I-829 application?

Based on your unique facts, it can be successfully argued that being on temporary Medicaid will not serve as a stumbling block for securing I-829 approval. However, it is advisable you should check with the right agency whether you qualify in the first place. The basic requirement for qualification is that a Medicaid applicant must meet the guidelines under the Affordable Health Act which is based on the calculation of the Modified Adjusted Gross Income (MAGI). Advisably consult a Medicaid expert who can help evaluate whether you meet the MAGI standard. The plan by the administration to change Medicaid and other government-supported programs under the public charge rule as it relates to immigrants remains in limbo as it has been suspended by a host of federal courts. In addition, besides Medicaid, consider signing up for any of the student health insurance programs in your school as an alternative or backup insurance plan.

I would look for a private insurance option rather than Medicaid.

The "public charge" law is on hold for now. It is proposed scope does not affect CPR status or naturalization applications, but it is not clear how this will move forward. As a side note, as a full-time student, you have access to subsidized health insurance through your school, which you likely can afford.

The public charge rules, that have been enjoined, and it applies to a person applying for permanent residence. You are already a permanent resident.