As far as service time goes, what happens when you sign an IFA at the very end of the season?  Does he accrue a year regardless of whether you play him or not?  Or will he stay at -0- years if you don't assign him?

If you don't assign him, you'll lose him at rollover.    If he plays in a game, even a playoff game, he'll accrue a pro year.

Have you (or anyone else) had enough experience with this particular situation to know if there's a benefit to not playing him?  After 6 seasons, I'm still not sure whether the game engine primarily doles out ratings improvements over an allotted amount of time (say, 4 seasons) or an allotted amount of game playing opportunities (4 seasons' worth of games = 536 minor league games).  Did this question make sense to anyone besides me?

It makes sense.   I don't think anyone should have a ton of experience in this.  I'm of the belief that players who play "partial" seasons don't develop the same as they would in the same time frame with a regular start.    However, from what I've seen, they lose a season of development.   An example:

Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Rashun Bryant

I drafted him in S11 and didn't sign him.  Another owner signed him before S12 started(during FA).   He didn't develop very well and, despite playing the entire season, his card doesn't even have a season 12 rating.

Does that answer make any sense to anyone but me?

No one has a rating for the first year of playing.  You also cannot trade an unsigned draftee who you signed in Free Agency until the next season.

Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Jimmy Ross

Jimmy is a guy I signed last season after he went unsigned during the draft.  He developed reasonably well last year.  I think Bryant might have a bit of a makeup issue also.

Thanks for the insight.  A couple of IFA's got signed after MILB playoffs had started in our world this season.  I'll watch them and report back if there's anything interesting to note.