If it's still cream/paste, meaning not powder or really dried out, it should be fine.
Over long time, the alcohol or liquids inside syringe can be absorbed the plastic of the syringe and the paste can become less fluid... but the original sealed syringe should suffer much less than a previously opened one.
Other concerns ... over time the contents may separate inside but a small syringe doesn't have enough volume and weight for that to happen or to be an issue. If you're paranoid, you may mix the drops of paste you put on the cpu with the tip of the syringe to get the paste homogenized (or whatever the word is).
So yeah, you should be fine to use that paste. I wouldn't worry that much about it.