As per Thaddeus Howze's answer, ships are definitely capable of FTL travel in the Alien universe. But I don't think the stasis pods are there for dealing with time dilation.
First, modern subs carry a year's worth of food and they are cramped and have limited space. Water is another issue but can be recycled easily as with the International Space Station. There is another reason for the stasis.
Keep in mind that FTL travel often means the space the ship is on is traveling faster than the speed of light, not the ship itself. So no time dilation would be experienced by the crew. See Alcubierre drive. The limiting factor for FTL travel would absolutely be the availability of exotic matter needed.
It is more than likely that in the Alien universe this matter is also extremely rare and extremely expensive to produce. Therefore some missions of great importance (the marines missions to investigate the lost colony) could be authorized to use FTL travel. Cargo missions would be relegated to using sub light propulsion and the necessity of stasis becomes paramount.