There is a certain test mentioned in Sanhedrin where Moshiach can 'smell and judge'. See here
בר כוזיבא מלך תרתין שנין ופלגא אמר להו לרבנן אנא משיח אמרו ליה במשיח כתיב דמורח ודאין נחזי אנן אי מורח ודאין כיון דחזיוהו דלא מורח ודאין קטלוהו
The Gemara relates: Bar Koziva, i.e., bar Kokheva, ruled for two and a half years. He said to the Sages: I am the Messiah. They said to him: With regard to the Messiah it is written that he is able to smell and judge, so let us see ourselves whether he, bar Kokheva, is able to smell and judge. Once they saw that he was not able to smell and judge, the gentiles killed him.
Bar Kochba failed this special (possibly prophecy based) test and was killed. I would venture to say that if he wasn't learned and couldn't judge at all, he wouldn't even have made it to that level of testing.
The fact that he is not quoted anywhere is not a proof to his being unlearned. To echo some comments on the question I would add that Rabi Akiva's own Rebi Nachum ish Gamzu is quoted only once (Berachos 22a) and yet we know he expounded the entire Torah by ribui and miut (Shevuos 26a).