Important to remember I'm not arguing here. Just think we all are getting our facts from different sources. I use the Halo Nation wikia. I can't find any mention of the UNSC Chara. Looked everywhere and all indications say the ship doesn't exist in canon. Now it is important to know that there are three major offenses noted on Arcadia,

- The first was the Insurrection in 2526, prior to the Human-Covenant War.
- In 2531 the Battle of Arcadia happened, in which the Covenant assaulted the world to obtain the Stellar Map at the Forerunner dig site you mentioned Foster.The UNSC was eventually able to push the Covenant off Arcadia. However the UNSC decided to abandon the world as a result of the battle, much of the civilian population being evacuated and all permanent Navel and ground forces being withdrawn. For the next 18 years the only settlement on Arcadia was the farming community of Abaskun.
- In 2549 the Covenant returned to Arcadia, and glassed the entire world after encountering no significant UNSC resistance.

The fact that it was noted that Abaskun continued to supply the UNSC means the at times there was atleast some UNSC presence. So the idea of someone being a soldier during the Fall of Arcadia isn't wrong. Just trying to point out that there was no second battle. It was more of a skirmish followed by its destruction.

http://halo.wikia.com/wiki/Arcadia