If I am looking a the right model Hp Envy 1534, you are using a HD 7570. I believe that GPU can support multiple screens.
If your only web-browsing, working on spreadsheets, Microsoft-word, and/or other things that aren't computer intensive than there isn't much of a downside to this, except the cost of the extra monitor. Your going to be adding more work for the GPU, but the things listed above don't push the GPU very hard.
If you are a gamer, than the issues get a bit more complicated. Using a second+ monitor for gaming is adding to the total resolution. Which means that the GPU is going to have an increased work-load. High-end GPUs can handle this on some games at high-ultra. This card is by no means high-end though, and you will likely have issues trying to run games with two monitors.