A referral can help your application get context and can be particularly useful when your profile does not sit inside a standard campus pipeline, but it does not replace the underlying qualifications.
For Master's candidates, the bigger question is whether you are applying through the right channel and timeline. Those pathways can differ from MBA recruiting.
Do not delay past an important deadline just to chase a referral. If someone knows your work well and can credibly explain why you would be a strong candidate, that is more valuable than a last-minute referral from a near-stranger.
Use networking to understand the office and role as much as to secure the referral itself.