If there's an advantage, it's inconsequential. If you want to avoid battles, wait until the 3rd cycle. On the 1st cycle, coaches contact recruits to gauge their interest. On the 2nd cycle, they make more serious recruiting efforts and you'll see many recruits considering. On the 3rd cycle, you'll have fewer battles.
If I only have money for one or two recruits, I often wait until the 3rd cycle or later.