For smoke tests it might work fine, but for true QA automation tests I would recommend duplicating as close to the final test environment as possible. I have seen false positives as well as missed bugs with variations which leads to a lack of trust in automated tests and simulated environments.
Usually cases for what you are suggesting and emulated mobile devices and such are for preliminary smoke tests on new functionality. Then a formal QA test run is done on the actual environment later. If that is the setup then the approach sounds just fine.