This works if the user ends up with 3% more balance than what he started with and do you think it is possible to do for 349 consecutive days?

In math we can derive lot of things but you need to understand the practical nuances that feels negligible but will make a huge difference at the end results and especially the whole strategy is build with the compunding effect so assume one bad day at 100th day and lost 50% of your balance then you need another 50 more days to make it up and one bad day will just keep ruining from this strategy to work.