Yes, you would have to drop and player from your roster to grab the FA thats on the DL. Then you can drop the pl;ayer you have on the DL to put the new player on the DL. But there is a chance that the first player you dropped will be picked up by another team before you get a chance to get him back. So unless you have a guy on your roster you dont mind losing, you may want o just hold tight.
A lot of this has to do with HOW the league was initially set-up (after the draft the setting cannot be changed) whether the option of player transactions is set for daily-today OR daily-tomorrow.
If your league is set for daily-today, you HAVE to remember that if you place a player on the DL that day, you have to place him on the DL FIRST, THEN pick-up the FA....if your doing a waiver claim, the slot MUST be opened the DAY BEFORE so the waived player has a spot to occupy.
Daily-tomorrow is a tad more complicated, say you shuffle your lineup on Monday and notice one of your players is now DL eligible. You can DL him THAT DAY, but your roster will carry 1 LESS PLAYER that day. Any FA claim will be eligible to play on your team on Tuesday. Waivers work the same way as above but of course add the extra day.