There is no interference. A key principle in EAP theory and application is that it does not interfere with normal administrative processes. This means that your attempts to manage your employee's job performance are not impeded by involvement in the EAP. You do not suddenly become unable to act as a result of making a supervisor referral. Likewise, the EAP will not direct or advise you as to what actions to take or suggest the types of disciplinary or administrative actions you should take in response to ongoing job performance or conduct problems.
It's your decision. Managing your employee's performance may include difficult decisions about how to respond to ongoing job performance or conduct problems. You may wonder about the "impact" or "effect" of certain administrative or disciplinary actions you plan to take. It is not proper practice for the EAP to advise, approve, or disapprove of proposed actions. To do so puts responsibility on the EAP for the outcomes of those decisions.