On the main ethereum network would the gas cost be the same to post several small transactions or one large transaction if the overall data size is the exact same?
Each transaction has itself gas consumption. Calculation of this consumption depends to codes that a transaction triggers them to perform and data size of the same transaction, so called arguments. For each transaction a bytecode is created. Processing each byte of this bytecode consumes itself gas. Hence, total gas consumption of the bytecode is equal to summation of gas consumption of each byte from that bytecode. This total gas is the same transaction's gas. Thus, each small transaction has itself bytecode and a large transaction has itself bytecode. One can conclude the transactions' gases are not equal together.