Regarding immersion, the term is generally referred to as hydrotherapy, and it comes in a few different forms. Sometimes it's simply immersion, sometimes it's contrasting between hot and cold water, and sometimes it's more along the lines of cryotherapy and ice baths.
There are numerous studies that offer minimal and mixed results. There is certainly no clear consensus. A recent study echoes most of the others in rather lack-luster results and no smoking gun:
Although results from passive and power tests were inconclusive in
determining whether cold water immersion or passive recovery was more
effective in attenuating fatigue, results indicated contrast baths had
little benefit in enhancing recovery during a cyclic week of rugby
Regarding inflammation in general and whether you should speed it up (heat, increased pressure, etc) or slow it down (cryotherapy, elevation, NSAIDS, etc), that's honestly still up for debate.
Inflammation is a natural body process and allows for an immune response. Dr. Gabe Mirkin, who coined the acronym RICE, has been trying to shatter it for a decade now. Her view is that it has been overused, new science has come out, and that generally speaking your body knows what it's doing regarding inflammation, particularly in the world of minor sports injuries.
- Cryotherapy and hydrotherapy have shown small negative, small positive, or no results.
- It's best to avoid interfering with the inflammatory response.
- There's little you can do to attenuate DOMS, but you can prevent it by regular exposure and avoiding eccentric actions.
The odds that you can out-think your body's inflammatory response is small, and the odds that you'll exasperate the situation, have no impact, or create side effects is larger.
What I've try to link to and base this answer on is rather objective data. There are high level athletes who do ice baths, but they might also eat broccoli at every meal: it's the classic point that correlation does not imply causation.