No. Time Machine deletes older files if they have been deleted from the source when it needs space on the backup drive for a new incremental backup. Time Machine "thins" it's backups; hourly backups over 24 hours old, except the first of the day; those "daily" backups over 30 days old, except the first of the week. The weeklies are kept as long as there's room.
How long a backup file remains depends on how long it was on your Mac before you deleted it, assuming you do at least one backup per day. If it was there for at least 24 hours, it will be kept for at least a month. If it was there for at least a week, it will be kept as long as there's room. By default, Time Machine backs up hourly. That cannot be changed in Time Machine. There are third-party utilities that will modify the backup interval such as Time Machine Editor.
The Time Capsule sparse bundle grows in size as needed, but doesn't shrink. Thus, from the user's viewpoint of the Time Capsule, it appears that no space has been freed, although there may be space in the sparse bundle.
Once Time Machine finds it cannot free up enough space for a new backup it reports the disk is full. You can either erase the backup drive and start over or get a larger drive.
All you can do is use the Time Machine application to delete the oldest files and folders from the existing backup until there is space then wait for the next backup cycle to start. But it would be simpler to just replace the backup drive with a new, larger drive and begin the backups from scratch.
Please visit Pondini's Time Machine FAQ for help with Time Machine. This is an extensive site with most everything you may need for using Time Machine. You will not find a better resource for Time Machine in one location. Due to the passing of James Pondini, the site is no longer being updated. Therefore, some of the information may be a little outdated.
