No, Chronologist is a SECOND chance at a recipe at the end of a mission. No idea what the chance for Chronologist is. I don't think anyone has hammered out details on the chance of regular Mission Drops.
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Originally Posted by Dispari
I don't know why Dink thinks she's not as sexy as Jay was. In 5 posts she's already upstaged his entire career.
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That's good news, the more chances the better, I guess - really don't feel like doing the math so gonna go with more chances=better. Also, according to this page of the wiki, http://paragonwiki.com/wiki/Recipes, Pool B drops are 10%. I'm not sure if that's accurate, but it's one of those number things I like.
I can give you my (completely just from my own experiences) take on this.
I "park" most of my toons in Ouroboros, just because it's fairly central travel-wise, and the Chronologist benefit isn't too darn bad. I've noticed that I receive a single recipe drop at the end of a mission well more than 50% of the time (I'd guesstimate about 60-70%), and I receive two drops probably about 10-15% of the time.
Not great drops, but like you said, more chances are better, and free is always nice. 
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StainedGlassScarlet - L50 Spines/Inv Scrapper | Badges: 1,396
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OK, I'm sold. I guess I'll be moving my guy tonight.
Its definitely significant. (50% is not a bad estaimte)
Inn addition Chronologist gives Pool A (mob drop), as well as or instead of Pool B.
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I assume (even though I know I shouldn't) that this badge increases the "normal" recipe drop chance for door missions completion (i.e. Pool B drops). Does anyone have a number for "chance to gain an invention recipe upon mission completion"? And is my initial assumption correct?
The only day badge I've cared about so far is Day Trader (I love being able to teleport directly to WW). However, I thought I'd invest the time to get this one if it's worth it, but it's hard to tell from the description.