To clarify, could a soldier of a lower tier, say a poor man that was a Velite, gain a higher rank (Hastati, Principe, Triarii, Equites, etc.) based solely on his performance in battle?
No. It wasnt a system of ranks (Velite to Hastati to Principe to Triarii to Equites) but rather a class system. Troops had to buy their own equipment, meaning the wealthiest were equites, as they had the money to afford and care for a horse. Triarii were nearly as wealthy, being able to afford armor, a shield, a spear, etc. Principe afforded some armor, a shield, and a spear. Hastati only had to buy a sword and a shield, with a small plate of armor. Velites were only required to bring a spear and a shield.
Now, you could say "Well, maybe they could be promoted!". But since the pre-Marian troops were not standing armies, promotion wouldnt be worth anything. Not only would you decrease the combat value of X group, you wouldnt really gain anything out of it except for that one campaign.
Sources: The History of Rome (earlier episode, will look through to find exact episode.) http://www.ancient.eu/Roman_Army/ (Recruitment area especially) http://en.wikipedia.org/wiki/Roman_legion#Roman_Republic_.28509.E2.80.93107_BC.29 (Outlines the classes better than i really could.)