The amount of caffeine in your cup will depend, as with any method, on the extraction time. It also depends on everything else, e.g. the grind, temperature of the water, but I can't find any information on what these typically are for Balinese coffee, so I'm going to assume they're the same.
Assuming you're using the same coffee with each method, the main thing that will vary is the extraction time. With pour-over methods, this will depend on the size and shape of the funnel, the porousness of the filter paper and the grind itself.
For Balinese coffee, there is no control. If you mix the coffee and water directly, the only thing limiting the extraction time is how long you wait before drinking it.
However, having said that, caffeine is actually extracted rather quickly. This study finds that routine percolation removes almost all soluble caffeine. However, the extended extraction time for Balinese coffee is likely to make a bitter brew.
In conclusion, no, you won't get more caffeine in Balinese coffee compared to filter. Both methods will remove almost all caffeine from the coffee.