Yes, they will. But if his baserunning ratings are low, he will get thrown out a lot trying for the extra base. Also, really fast players beat out a bunch of infield hits, even more if they have excellent contact ratings.
Cobb & almost all pre-1920 players were low-percentage base-stealers (by today's standards) and should be 0s & 1s in this sim. In those times, with home runs rare occurrences, runners needed to be on second to score on a single. Also hit-and-run plays (where runners are usually thrown out if the batters do not make contact) were far more common pre-1920.
If those players played today's game, their SB attempts would be way down and their SB% would be way up. Another place where the sim could use normalization.