The cup draw only takes in account the average quality of the 14 highest quality players.
Not signing free agents is tricky, since once the roster reaches 14 or 15 (can't remember exactly) managers are no longer allowed to auction/release players. Therefore, getting the 3* free agents quality applied for cup draw purposes, you'll actually have to sign them so you can auction/release players.
Personally, I like to sign and keep the 0T academy players for this purpose. They're young enough, that I can get extremely low Q players on my roster if I constantly promote. A 2* 18 yr old that promotes every season is a 1* 28 yr old for a manager 9 levels below your level.
Back to the league quality; I noticed a team on my friends list at my level, is facing a team that is last place in his league in the champions league Quarterfinals. This last place squad only a has a negative GD of -14 (10 Goals, 24 GA), so he isn't tanking. I think they're definitely basing league draws on quality now. It will also water down the champions league draws for next season I believe.