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Actually it will run slow as molasses.
Have you used a web browser in the last few years? Give me a break. It is crazy how slow to load and respond many simple desktop apps are. Unless you are doing something very graphically intense (like a game) you can get 100% adequate performance with way less effort using html5. It will definitely be faster to load and use less memory than a gtk app. Edited 2013-05-29 05:21 UTC
I think you are confused as to what exactly makes web browsers sometimes run faster and use less memory.
For a simple example, the Gnome calculator weights 8.4 MB, whereas merely opening a new tab in Firefox without doing anything in it costs 11 MB. With this in mind, I strongly doubt that you can make a calculator web app which weights less than the Gnome one.
Same with performance, it really depends on if you are dealing with crappy coders and/or use an OS that has a poor file management performance. Most of my basic apps show up in about a tenth of a second, which is already a lot but far from being unacceptable. Edited 2013-05-29 06:10 UTC