This is an interesting question, however, it does lack a proper clarification what is considered a convolutional neural network.
Is the only requirement that the network has to include a convolution operation? Does it have to only include convolution operations? Are pooling operations admitted? Convolutional networks used in practice use a combination of operations, often including fully connected layers (as soon as you have a fully connected layers, you have theoretical universal approximation ability).
To provide you with some answer, consider the following case: A fully connected layer with $D$ inputs and $K$ outputs is realized using a weight matrix $W \in \mathbb R ^{K\times D} $. You can simulate this operation using 2 convolution layers:
The first one has $K\times D$ filters of shape $D$. Element $d$ of filter $k,d$ is equal to $W_{k,d}$, the rest are zeros. This layer transforms the input into $KD$-dimensional intermediate space where every dimension represents a product of a weight and its corresponding input.
The second layer contains $K$ filters of shape $KD$. Elements $kD\ldots(k+1)D$ of filter $k$ are ones, the rest are zeros. This layer performs the summation of products from the previous layer.
Such convolutional network simulates a fully connected network and thus has the same universal approximation capabilities. It is up to you to consider how useful such an example is in practice, but I hope it answers your question.