Yes. Free-to-Play (F2P) and Preferred players gain XP (experience) slower than Subscribed players, but not until level 20. At level 20, subscribed players will gain XP 20% faster than Free-to-Play or Preferred players. Before level 20, all players receive experience at the same rate.
The good news is the rate at which experienced is gained is fairly fast for all players, and players should not have to worry about being under leveled unless they are only doing the main quests. Free-to-Play and Preferred players should have no problems keeping up with the level of their quests as long as they do all purple quests they come across and a few quests here and there on the side. Subscribed players will rarely, if ever, have to do quests outside their main storyline and planetary storyline (the purple quests) to keep up with the suggested level of their storyline.
The developers of Star Wars: The Old Republic have also made it even easier to level with level sync – if the planet you are on is rated at a lower level than you currently are, you will still be able to gain experience from any quests you choose to take on, and any enemies you fight. In return you will be “synced down” to the level of the planet, so you will never be “overlevelled” on a planet.
If you ever do find yourself running short on experience, an easy way to do this is by completing some heroics which grant great XP and credits. Heroics can be picked up from terminals near where you load in to the planet, or from a large terminal in the Combat section of the fleet.