In the case of your image? Absolutely not. A lot of time when dealing with cylindrical objects though, having some extra loops helps. Here is an example of something I did a while back: Here, you can see that I made the carousel by making one section of it, then copying it and bending it into a round shape. Since it was…
If you are cutting in edges on a model with a tiling texture that has previous uv's, the placement of the edges can affect how the texture reacts. However as earthquake mentioned, remapping the uv's will fix any stretching. To give you a real world example, if you slice off the top of a pillar and add damage modeling and…