Remember that you aren't suspended for a certain number of games. Rather you are suspended until such time as your first team have completed x number of qualifying domestic games, there's a subtle difference. Therefore, even though the Checkatrade doesn't count towards your suspension, you can't play in it as your first team haven't completed x number of domestic games.
Comparing it to the Champion's League doesn't work s that isn't a domestic competition and suspensions are handled by a different authority. As I said before though, it needs a rule change as it is unfair on the lower league teams who enter their first teams as opposed to Premier League and Championship teams who put their U21s in.