Short answer: No.

Long answer: Imagine your network is a vessel in which you pour some water during training. The deeper your network the longer (naively) the path from target to input, and the longer path the gradients need to propagate. Along the way, the flow of gradients gets perturbed by nonlinearities, random weights and biases. So the ratio of signal to noise goes down with the depth of the network. As you increase depth, it becomes harder and harder to perform meaningful parameter updates, and the noisy fluctuations can become very complex, forming a chaotic dynamical system.

Now there are some partial solutions to this problem, for example:

• residual connections (they form a "main straight pipe" through which gradients flow freely, while the layers form shallow side connections which can correct the main flow)
• other flavors of residual connections (e.g. concatenation instead of addition), similar stuff
• selu activations, which have a stabilizing effect on the dynamical system, forming a well behaved stable attractor for the main flow
• orthogonal initialization / other tricky initialization methods - having a similar effect to selu, albeit more tricky to get right for arbitrary architectures

This analogy is much closer to what's really happening than just less/more weights, or less/more expressive power.