Yes, they can, but no they won't turn out world class. Every player has some form of ability, and that ability can lead to a good performance. Take Chris Herd for example, back in FM 2010 I had him on my reserves team at Aston Villa. He was horrible as a player, according to my scouts. He would only be an average player in League 2, they told me. And first year, he tore apart the midfield in the reserves league. Then I loaned him out, to a top League One club, and he tore up the midfield there as well, proving my scouts wrong. I was proud of him, and he led that club to third in the end. So I offered a new contract for another three years, and I was looking forward to seeing how he advanced.
I tried a couple games with him on our first team, and he performed just as he was rated, ****. But, when given a chance in the reserves or on a Championship or lower team, he could exceed all expectations.
If there is a player in particular that you want to give a chance, whether that be because you like his stats or like his name or because you just like the player, give him that chance and wait a little while. There's no guarantee they'll be of any use, but there's no real reason why a League Two player couldn't perform decent in the premiership. But, to put this in perspective, out of all my other half star rated players, none became any good anywhere, except one young regen striker, who was only half star rated but scored at least once in every youth game. Once he was promoted to the reserves, he played horrible though.
So, in short, yes they can, but their star ratings and potential cannot be risen. Their stats will not dramatically sky-rocket, and your scouts won't see the error of their ways and tell you not to sell them. The player could be performing with a 9 average over a whole season, and none of those things will happen.