No, as Rious stated, you only need to have the all access pass. You can buy the subscription or consume a Krono for 30 days of game time and you must keep your subscription up. If it lapses then you will not be able to login to that server until you get all access again.
if you make multiple characters on a progression server, write down the account/name/class and keep it somewhere you can find it months later. Very often people take a break then cannot remember which character they had on which server. As you cannot log in to check it becomes a guessing game on who is where.
There is a file in the EverQuest directory called something like <account name>_characters.ini that should list the character names you have on that account and which server they're located. However, Moege's suggestion is still good since you may not remember the character's name that you're after. Also, if you delete that file or the directory, you're written notes will be all you have.
DB now creates a file in your EQ directory that lists all of your characters and sever. In your eq directory there will be a file called <your login name>_characters so if your login is Bilbo28 the file will be Bilbo28_characters Character0=name1,agnarr Character1=name2,agnarr Character2=name3,agnarr Character3=name4,agnarr Character4=name5,firiona Character5=name6,rathe Character6=name7,antonius etc Gialana beat me to it...