First Back to Back races one day after the next?

First, there’s no ”speeding up” recovery.  Being aggressive in the prologue will significantly affect your second day race.  Even being very conservative will likely have *some* impact on the OLY, much of which will show up during the run.  

There are plenty of people who successfully race back-to-back although “race” may be a misnomer.  Back in 2010, I did a Friday night marathon and Saturday 30 mile trail run.  My strategy was to go real easy on the marathon, walking up hills, etc. The nice thing is that marathon was a “prediction run” so no watches, GPS, course clock, and the “winner” was the last person to finish before midnight.  My running partner and I finished in 5:18 where we often ran <9min/mile pace and had run a 4:10 marathon.  

My suggestion is to plan your prologue goals and race strategy around hitting time targets (like road rallying).  Maybe you can normally swim 250 yards in 5 minutes and run 8:00 miles...make your prologue goals 6:00 and 10:00 and hit those consistently.  Think of it as an exercise in “race discipline “  where you’re managing early exertion.  

This depends totally on you: What your level of fitness is, how often you're accustomed to putting out max efforts, and how rested you are going in. And maybe your age...

When I was at the top of my tri game, it wasn't too strange to do back-to-back sprint tris in a weekend. Sometimes performance on the second day was better than the first. Ah, to be young and indestructible.

When I was bike racing, we often would have three to four racing days a week in peak season, with a criterium on the last day. My fitness was to the point where it would take a good hour to warm up to be ready to race. And yes, besides a full-time job, bike riding/racing was pretty much ALL I did... We won't go into the effects on the rest of my life...

No way I could do that now.

So I say go for it, see how it goes, and warm up slowly into that second day.

Good advice above and I'll add that many training plans have a day-before-the-race short effort with some intensity (though I think you're pushing the limit/definition of "short" because you also need to account for some warm up and cool down).  Be sure to taper well and I would take off the day before the prologue for sure.