. . .
I don't think the Service Corps exists yet at this point, since the one you seem to be speaking of was organized from the Ruusan Reformation.
The Service Corps was considered an honorable alternative to serving in the Army of Light or the mainstream Order following the Ruusan Reformation and the defeat of the Dark Lords of the Sith. Organized under the Reassignment Council, the Corps was made up of four branches: the Agricultural Corps, the Medical Corps, the Educational Corps, and the Exploration Corps. Membership in each was voluntary and many ranking members of the Order joined, but if an Initiate had failed the Trials, the Council took care of assigning them based on different skills and requirements.
The system of government did not seem to change too dramatically (as the Republic had been ruled by a Supreme Chancellor and the Galactic Senate as early as 15,000 BBY) but the Jedi Order underwent a significant adjustment. In symbolic measures, largely to convince the Republic that they would not become a conquering army, the Jedi abandoned their battle armor, renounced all military ranks (such as "Jedi Lord"), dissolved their commander-in-chief, disbanded their army, naval and starfighter forces, and placed themselves under the supervision of the Supreme Chancellor and the Judicial Department, effectively dissolving the Military. In order to lessen the chance of a Sith resurgence, the Order began training children from birth. In addition, the training of Padawans was centralized on Coruscant, to remove the danger of unsupervised students delving into forbidden Sith knowledge.
So it seems that at this point in the Republic, it's fully possible to become a Jedi, even if you were discovered at an adult age to be Force Sensitive.
EDIT: Ruusan Reformation is *long* after the TOR-storyline, after the complete fall of the Sith Empire, the emergence of the Brotherhood of Darkness, and during the rise of the Rule of Two-Sith.