I will split this answer into two parts - first, about sensory immersion as it is defined and scientifically examined. Second, I will try to address specifically what you asked for regarding the effects of sensory overstimulation and overload.
I don't think your definition of sensory immersion is right when you said it's a "deliberate overstimulation". There is an excellent perspectives' paper in Science, where the author refers to common definition of immersion as the subjective impression that one is participating in a comprehensive, realistic experience (Dede, 2009). So you don't need to be overstimulated to experience immersion - you just need a specific context and environment for it. Quick literature search indicates that the study on sensory immersion has been mainly focused around computer games and virtual environments. Dede (2009) describes a number of examples, arguing that immersion in a digital environment can enhance education by allowing multiple perspectives (Salzman et al., 1999), situated learning (Clarke et al., 2007), and transfer. For example, students can model expert's actions to better learn how to perform surgery, using sophisticated virtual reality with tactile surgery robots. Or they test different epidemiological hypothesis in an online social games like River City.
Immersion has also been linked with flow-like experience in computer games. Nacke & Lindlay (2008) asked participants to play Half Life 2 while they were measured with electroencephalography, electrocardiography, electromyography, galvanic skin response and eye tracking equipment. They demonstrated measurable high-arousal positive affect emotions during intensive combat level in the game. There is extensive literature on that topic that examines cognitive effects of computer games.
The effects of sensory overload is quite a different story. Lipowski (1975) argues that overstimulation increases as a direct consequence of the accelerating pace of technological advance. Author points to the numerous sources of overstimulation including overcrowding, noise and work load (Lipowski, 1975). One the largest set of experiments on sensory overload has been conducted in Japan. Behavioural effects of sensory overload included heightened and sustained arousal, mood changes in the direction of aggression, anxiety, and sadness (Kitamura et al., 1970; Hatayama et al., 1970). Some participants reported visual hallucinations. Authors also found that participants strongly preferred sensory deprivation to sensory overload (Kikuchi et al., 1970). Other studies showed that exposure to sensory overload produced an increase in the scores on the scale of social alienation/personal disorganisation as well as in the cognitive/intellectual-impairment scores (Haer, 1971; Gottschalk, 1972).
Therefore, from the cognitive standpoint, it's difficult to see benefits of sensory overload. You mentioned the music as a potential factor, and indeed some empirical studies showed music can improve reading comprehension (Kiger, 1989), and contribute to higher performance in repetitive tasks (Fox, 1971). But majority of the studies clearly showed that such positive effects are only possible with low-volume and low-level of 'information load' in music (like speed, lyrics, etc.). Also, while I don't doubt your positive personal experience with dichotic listening, the studies clearly show that it has mostly negative and distractive effect on the attention (Asbjornsen et al., 1995).
It is also difficult to find studies showing that dissociative state caused by sensory overload could benefit meditation. Studies shows that meditation is specific in its ability to reduce distractive and ruminative thoughts and behaviours (Jain et al., 2007; ). Meditation aims at giving you better control over your attention, and I don't see how that could be achieved with heavy level of sensory distractions around you.
I like your question and I understand your intuition behind it, but the research seem to indicate that sensory overload is mostly a negative experience and it is unlikely that it contributes to enhancement of cognitive functioning.
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