In this paper, we evaluate outage probability (OP) and intercept probability (IP) of an Intelligent Reflecting Surface (IRS)-aided Non-Orthogonal Multiple Access (NOMA) system employing Fountain Codes (FCs). In the proposed scheme, a base station (BS) simultaneously transmits two encoded packets to a near user and a far user in the presence of multiple eavesdroppers. Specifically, the BS directly sends encoded packets to the near user, while the far user receives encoded packets via the IRS. Both users and the eavesdroppers attempt to collect a sufficient number of encoded packets to reconstruct the desired data before the data transmission of the source ends. In addition, the eavesdroppers are assumed to collude by sharing the intercepted packets. We derive exact closed-form expressions of OP and IP over Rayleigh fading channels, and investigate the trade-off between OP and IP.