Can a representation of Matrix Lie Groups be understood as an embedding?

Question

A representation is a homomorphism $$ \Pi: G \rightarrow GL(V)$$ $GL(V)$ is a matrix Lie group and we could regard it as $\mathbb{C}^{N^2}$ if $V$ is a $N-$dimensional complex vector space. So the question is if we could say that a representation of $G$ is an embedding of $G$ in $GL(V)$