Was your account active yesterday? The only thing that matters is that your account is active from Feb. 1st all the way up to April 18th. If you cancelled your subscription with playtime left, then set up your monthly subscription before your last playable day you're fine. However, if your account becomes inactive for even one day during the specified period, you're out of luck.
As far as I'm aware, you should be fine as long as our account doesn't become "unplayable".. and even then, they might allow something like 24 hours for re-subscription if you didn't realize it was about to run out. I've heard of people /petition'ing the reward in certain circumstances like that.
Even though you had no payment info, if you were still "Playable" yesterday, you should be fine.
Oh yeah it was playable till some point in March. Thanks a bundle for the info 
As Master-Blade said, you just need to keep an active account. It doesn't matter if you have billing info on file. As long as you don't receive the email saying that your account has been deactivated for "payment termination or failure", then you're all good.
Also, don't get banned. I'm pretty sure that even a 3-day will make you inelegible, because the requirement usually includes a line about having an "active account in good standing".
@Roderick
I think around March of last year I signed up for a one year payment deal for City of Heroes. A few days ago a canceled the subscription so I would remember to convert it back to a $15 per month type of deal. And I just reactivated it today. Will I still get this Super Rewards thing? My game time was still active but I didn't have my billing info in at the time.