Answer
Yes, for two parallel vectors in the same direction $\lambda \vec{v}=\vec{u} , \lambda>1$
Work Step by Step
Yes, it's possible. Let $\vec{v}$ and $\vec{u}$ two parallel vectors, and then
\[
\begin{aligned}
\lambda \vec{v}=\vec{u} \Rightarrow \quad\|\vec{v}+\vec{u}\| &=\|\lambda \vec{v}+\vec{v}\ |=\|(1+\lambda) \vec{v}\| \\
&=\|\vec{v}\| |1+\lambda|
\end{aligned}
\]
For $\lambda>1$, we have two parallel vectors in the same direction and
\[
\begin{aligned}
\|\vec{v}+\vec{u}\| &=\|\vec{v}\|(1+\lambda)=\|\vec{v}\| +\lambda\|\vec{v}\|\\
&=\|\vec{v}\| +\|\lambda \vec{v}\|=\|\vec{v}\|+\|\vec{u}\|
\end{aligned}
\]
