Can Naruto go into Sage Mode repeatedly by using idle shadow clones?
Every time shadow clones are created, the user's chakra is divided equally among the clones. If a clone creates further shadow clones, that clone's chakra would be evenly distributed among the newly created clones.

According to what Frog Sage Fukusaku explained to Naruto, to enter into sage mode, the user needs to gather natural energy while balancing it with one's chakra. It is difficult to maintain that balance with lower chakra. The user turns into a frog if the natural energy overwhelms the user's chakra. Moreover, if any of the shadow clones turns into a frog, the original user too turns into a frog. 

Hence, repeatedly making shadow clones to go into sage mode increases the risk of turning into a frog, and hence, Naruto cannot use this trick practically.