You do not have to be honored to drop a suspension tier. Basically, you just need to play games without racking up reports. It's perfectly fine to say things like "gg" or to give your teammates compliments, in fact those are considered to be signs of good sportsmanship and qualities that Riot encourages its players to display.
The link that MP edited in is a really good one, where Tantram explains a bit more about how there is no definite time-frame regarding how long it takes a player to drop tiers. I've seen people come to the Boards posting about how they were permabanned anywhere from 1 day to almost 9 months after their 14 day suspension. In the case of someone that took 9 months, they didn't play much so they never earned any "positive" credit on their account and their next big infraction was enough to push them back over the edge.
It's really good that you've come here asking questions now, while it's still possible to change things and before it's too late. Best of luck in the future!