Playing a man defense, a player can still be effective with low stamina. But if you were playing a press, 60's stamina might let that player be effective for much shorter stints. And if you run fastbreak-press, stamina matters even more.
If the issue is that you just don't see this recruits stamina, without actually studying the data, I would say it's very rare for a recruits stamina to max out below 65. It can definitely happen, but I think it's very rare. So if you are looking to recruit a player without seeing his potentials and he's currently at a 60 stamina, I think it's fair to assume that he has at least average potential.