Here's a very small quantitative sample of actual frequencies of runners on 2B attempting to score on a single. I looked at the first 61 games (up through the amateur draft) of my team in Hamilton NL. Then I got bored...
I was a bit surprised how few of these situations arose. Only 51 times in 61 games:
0 Outs 7 events / 4 attempts to score/ 1 time thrown out
1 Out 19 events / 11 attempts to score/ 1 time thrown out
2 Outs 25 events / 19 attempts to score / 1 time thrown out
0 Outs 71% attempts to score/ 80% success
1 Out 58% attempts to score/ 91% success
2 Outs 76% attempts to score / 95% success
These admittedly small sample size percentages are not very different than the actual MLB rates I posted above. The success rates are a bit low, but I had my managerial settings on 4 for baserunning aggressiveness, and one less time thrown out would put the HBD numbers right at the MLB rates.
Player speed ratings definitely make a difference. 5 guys with speed ratings < 40 attempted to advance 50% of the time, overall (9 of 18), and got thrown out twice; The other 5 guys, all with speed ratings over 75, attempted to advance 78% of the time (26 of 33) and got thrown out once. I didn't see much dependence on baserunning ratings, but I didn't have as much spread in player ratings either, and I didn't really crunch any numbers.
This NL team was decent offensively, but not great - within +/- .005 of the world average in BA / OBP / SLG. Was about .550 winning % midway through the year, but mostly with pitching. 110 SBs, 55 CS on the year. And we played in a neutral park.
This work wouldn't pass muster at a SABR convention, but I've satisfied my own curiosity as to whether HBD closely approximates MLB or not in regards to runners attempting to score from 2B on a single. I think it's about right.