In the DJ world we have something called Digital Vinyl System ("DVS"). DVS allows you to use time-coded vinyl to control playback of digital files on your turntable. DVS has a latency measured in milliseconds (while true analog vinyl has no appreciable delay at all.) Where the delay really becomes an issue is with scratching because of all of the fine motor skills involved. Anyway, the reason this is applicable here is because when using DVS you get a good idea of how much a few milliseconds in delay can affect your ability to accurately reproduce movements that have no delay in the analog realm.
Like others have said, 1.5 ms of delay is not very much delay. It's so small that many people would not recognize it at all. However, as some others have responded variability in the delay can be a real problem. I'm a fairly advanced scratcher and the latency on my system is about 6 ms, which is perceptible but not so much that I can't adjust. It's not perfect, but it's pretty darn good. That being said, its VERY important that the delay is not variable because the reason you can deal with 6 ms of delay is because your mind and body adjust to accommodate that 6 ms. So, while my mind and body only take a few seconds to adjust from true analog vinyl to 6ms of delay in DVS, I suspect that wouldn't work if the DVS delay was a moving target. I can tell an appreciable difference between 4.5 ms delay and 6 ms of delay when doing a back-to-back A/B comparison, meaning that variability would likely be distracting. The main reason I believe that 6 ms doesn't ultimately matter too much is that it's a CONSISTENT 6 ms. Once your body adjusts then the mind just knows that everything is going to be 6 ms off and you forget about it. I imagine the 1.5 variability could really throw things off (especially for more advanced players) because your mind and body can't adjust properly.