Can the plus operator in regex be replaced by the star operator?
True. For any regular expression $R$, (the meaning of) $R^+$ equals $R \cdot R^*$, and conversely, $R^*$ equals $R^+\mid\varepsilon$ (where $\mid$ here is the choice operator 'or', and $\varepsilon$ the expression matching the empty string).  

Thus in any regular expression dialect it suffices to include only one of star and plus without loosing expressibility. Translation of plus into star can be done recursively (inside-out).