No. Variables are emptied and re-initialized between test executions.
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Why automate? I do automated testing because there's only so much a human being can do and remain healthy. Sleep is a requirement. So, while people sleep, automation that I create does what I've described above in order to make sure that nothing gets past the final defense of the testing group. I love good food, good books, good friends, and good fun.
Object type variables have global visibility scope and can be used to obtain an object from any keyword test or script unit or to exchange data between tests or units. These variables are available even when a test run is terminated and script variables do not exist.
If all your steps are being run in one pass inside one project or project suite, then you have project variables or project suite variables that will persist. Once the test run ends, then the values are gone.
While generally speaking this might appear to be possible (your description is just not detailed enough), persistance of the variables that keep references to UI objects is far not the best practice.
The reason is that if the referenced object is re-created by the tested application, its reference that is kept in the variable will be invalidated. This will result in .Exists property to return False and test code will need to search for the new object again.
Exact implementation of test code (its architecture) obviously depends on your knowledge of the tested application internals, but you need to keep in mind the above details.
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